







0/0 
20160214 

From Noni: Q. 0÷0=1 Why it is wrong when 4÷4=1; 3÷3=1; 2÷2=1: 1÷1=1 ? Answered by Penny Nom. 





The zeros of a fourth degree polynomial 
20130123 

From Dakota: My problem has multiple steps and I have done everything but the last one. 8The original problem is f(x)=x^45x^3+7x^2+3x10 and I have to find the zeros of the equation. I used synthetic substitution like my teacher taught us to get the equation of x^33x^2+x+5=0 but now I don't know how to get the zeros of that equation, or solve it. Answered by Penny Nom. 





A parabolic arch 
20120104 

From Swathi: A plan for an arch in the shape of a parabola is drawn on a grid with a scale of 1m per square.
The base of the arch is located at the points (0,0) and (15,0). The maximum height of the arch
is 18m.
a)Determine the quadratic function that models that arch
b)State the domain and range of the function Answered by Penny Nom. 





The graph of a quadratic function 
20111227 

From Thomas: sketch a quadratic function with zeros at 3 and 1 Answered by Penny Nom. 





1 divided by 0 and infinity 
20111024 

From ritika: we say that one divided by zero gives us infinity, then why zero multiplied by infinity does not gives us one????????????? Answered by Robert Dawson. 





What is x to the power of 0? 
20110323 

From Jason: What is x to the power of 0? Answered by Robert Dawson. 





A product of 1 000 000 
20101119 

From Sharron: There are many pairs of numbers that when multiplied together give a product of 1 000 000. However, there is one pair, and only one pair, of whole numbers that contain no zero digits and has a product of 1 000 000. What are these two numbers? Answered by Stephen La Rocque. 





z^5  3z^4 + 2z^3 + z^2  3z + 2 
20101106 

From Kumar: would you please solve this problem, related to complex numbers.
Find all the roots of :
z^5  3z^4 + 2z^3 + z^2  3z + 2 Answered by Robert Dawson and Penny Nom. 





Terminal zeros 
20101104 

From morgan: if I have to multiply 1*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18*19*20 how many terminal zeros do i get? Answered by Penny Nom. 





A fourth degree polynomial function with real coefficients 
20101030 

From Ryan: Question from Ryan, a student:
What is the fourth degree polynomial function with real coefficients
that has 1,1 and I as zeros and such that f(x)=160 Answered by Harley Weston. 





A polynomial with integer coefficients 
20101023 

From Adori: Question from Adori, a student:
Find a polynomial with integer coefficients that has the given zeros: 2/3, 4, root of 3i, root of 3i. Answered by Harley Weston. 





Complex roots 
20100414 

From Lan: If b and c are real numbers so that the polynomial (x^2) + bx + c has 1 + i as a zero, find b + c. Answered by Penny Nom. 





How many zeros? 
20100318 

From jeff: 1 light yr is 6,500 billion miles, the galaxy "Andromeda" is 2,500,000 million light yrs, how many zeros are in this equation ? Answered by Robert Dawson. 





Factors and zeros of a polynoial 
20100317 

From Susan: find a polynomial function of degree three with 3 as a zero of multiplicity 2 and 4 as a zero of multiplicity 1. Answered by Tyler Wood. 





Zeros of a polynomial 
20100301 

From Gavin: Suppose the polynomial R(x) = a_9x^9+a_8x^8+...+a_1x+a_0 has real coefficients with a_9≠0. Suppose also that R(x) has the following zeros:
2,
3,
i
Using this info, answer the following.
a. What is another zero of R(x)?
b. At most how many real zeros of R(x) are there?
c. At most how many imaginary zeros of R(x) are there?
p.s. I used _ for subscript
thanks so much Answered by Harley Weston. 





The zeros of a polynomial 
20090925 

From jordan: find a polynomial of lowest degree with only real coefficients and having the given zeros.
1+2i, 2 (multiplicity 2) Answered by Penny Nom. 





Zero Angle 
20090901 

From Nazrul: Is zero degree an acute angle? Please explain. Answered by Janice Cotcher. 





The last non cero digit of a factorial 
20090612 

From Wilson: How can I find the last non cero digit from a factorial calculation of a big number.
For example 10! = 3628800, the last non cero digit is 8.
What is the last non cero digit of 10! ?? Answered by Robert Dawson. 





Find a polynomial function with the indicated zeros and satisfying the given conditions 
20090323 

From Kristen: Find a polynomial function with the indicated zeros and satisfying the given conditions. Simplofy your answer (no imaginary numbers or parentheses in the answer)
Zeros: 1+2i, 12i, 5 ; f(2)=1 Answered by Harley Weston. 





y = p q^t 
20090212 

From Conor: y= p x (q (to the power t) ) ; y= 100 when t = 2 and y= 4 when t= 0
a) find p and q
b) hence find y when t=4 Answered by Stephen La Rocque. 





ax^2 + bx + c = 0 has no real roots and.... 
20090126 

From Alberto: The equation ax^2 + bx + c = 0 has no real roots and a + b + c < 0 . Chose the right answer:
(A) c > 0
(B) c <= 0
(C) c = 0
(D) c >= 0
(E) c < 0
Explain the choice. Answered by Robert Dawson and Harley Weston. 





Real and imaginary zeros 
20081112 

From David: Find all the real and imaginary zeros for each polynomial. Factor each polynomial. Leave factors with imaginary zeros in quadratic form.
h(x)= x^5 +2x^4  10x^3 20x^2 +9x + 18 Answered by Harley Weston. 





Is zero a number? 
20081021 

From milan: why people call 0 number?....0 is nothing. What is 1,2,3,4,5,6,7,8,9?than???this is not logic...thanks i dont know what else
number means quantinty,but 0 means nothing.Thanks Mialn Answered by Harley Weston. 





Is zero a perfect square? 
20080814 

From peter: is zero a perfect square? Answered by Penny Nom. 





Why can't you divide by zero? 
20080804 

From Donna: Why can't you divide by zero? Answered by Chris Fisher. 





Is zero an even number, an odd number, or neither? 
20080804 

From Donna: Is zero an even number, an odd number, or neither? Why? Answered by Victoria West. 





The positive real zeros of f(x) = x^4 + x^3  7x  1 
20080606 

From CiCi: How many positive real zeros does the function f(x) = x4 + x3  7x  1 have? Answered by Janice Cotcher and Harley Weston. 





Zero divided by infinity 
20080503 

From ANNE: There was a question about what do you get when you divide Zero by infinity. There was an example using Potatoes. Could someone please explain a little bit more in detail, so that I can help my son who has Schizophrenia understand. He is big into Mathematics and is consumed by this question.
Thankyou so much,
Anne Answered by Penny Nom. 





Division by zero 
20080501 

From Bill: Why does multiplication have a favored status so as to make division by zero undefined? Answered by Harley Weston. 





For what values of a does x^313x+a have 3 distinct roots? 
20080425 

From Jyotishman: What can be the value of a for the equation to have 3 roots?
x^313x+a=0 Answered by Harley Weston. 





The zeros of a cubic 
20080409 

From Ryan: what are all the zeros of f(x)= x^31/2x^2+1/3x1/6 Answered by Penny Nom. 





2 times 0 times 0 times 4 
20080330 

From ben: what is 2 times 0 times 0 times 4? Answered by Penny Nom. 





Why is the number 1 neither prime nor composite? 
20071108 

From amarilis: why is the number 1 neither prime nor composite? Answered by Penny Nom. 





Finding the last nonzero digits of large factorials 
20071004 

From Mukesh: i have to find last five non zero digits of integer which can be very large (
upto 10^12) . i can find last non zero digit of of any factorial. Now my problem is that
i have to find last five non zero digit of factorial and also i want to general method for
last K non zero digits of factorial n. For example 10!=3628800 so last non zero digit is 8 ,last two
non zero digit is 88 .....and last five non zero digit is 36288. Answered by Victoria West. 





What feature on a graph shows the solution? 
20070819 

From San: To solve the equation 2sinx+square root 3=0, what feature of the graph,
in the form y=asinx+b would show the solution? Draw a graph to show
the solution. thanks. Answered by Stephen La Rocque. 





f(x) = (x^4)  4x^3 
20070722 

From Michael: I'm a student who needs your help. I hope you'll be able to answer my question.
Here it is: Given the function f(x)=(x^4)4x^3, determine the intervals over which the function is increasing, decreasing or constant. Find all zeros of f(x) and indicate any relative minimum and maximum values of the function.
Any help would be appreciated. Thank you for your time. Answered by Harley Weston. 





A polynomial with integer coefficients 
20070620 

From Krys: How do I find a polynomial P(x) with integer coefficient that has degree 4 and zeros 12i and 1 (with multiplicity of 2)? Answered by Penny Nom. 





Is zero a number or a place holder? 
20070409 

From Chris: Is zero a number or a place holder? Answered by Penny Nom. 





Finding the xintercept 
20070302 

From Ash: Y = 1/100X^2 =27/10X +0 = 0 THE Y INTERCEPT IS 50 HOW DO I FIND THE X INTERCEPT Answered by Gabriel Potter. 





2/3 to the power of 0 
20070225 

From Adam: (2/3) TO THE POWER OF 0 Answered by Penny Nom. 





Multiplying and dividing by zero 
20070205 

From colin: i would like to if u multiply 1,000,000 by 0 does it equal o or 1.
if you have a number eg 15689 and you divide by o what would the answer be is it 1 Answered by Penny Nom. 





Zero as an exponent 
20061028 

From Don: Any real number (except zero) to the zero power equals 1 correct? Question: If for example x to the zero power equals 1 What is x to the zero power equal to? What is (x) to the zero power equal to? Answered by Penny Nom. 





How can we explain to middle school students that 0^0=1? 
20061015 

From Peter: How can we explain to middle school students that 0^0=1? Answered by Steve La Rocque, Penny Nom, Claude Tardif and Harley Weston. 





A base number raised to the power of 0 
20060824 

From Sheila: I'm a 5th grade teacher and need some help with a base number raised to the power of 0 always being 1. My kids asked me why and I told them I'd find out. Answered by Penny Nom. 





The zeros of a function 
20060612 

From Sky: find all the real zeros of the function:
f(x)=2x^{3} + 4x^{2 } 2x  4 Answered by Stephen La Rocque. 





Is zero even or odd? 
20060404 

From Aliya: I would like to know if zero is an odd number or even number. I remembered my kindergarten teacher saying it is an odd number. My mom and sister says it is even number. Answered by Penny Nom. 





1/infinity and 1/0 
20060304 

From Evan: I was thinking the other day when i was in math class that when you divide 1 by say n you'll get 1/n. As the value of n increases the smaller the number you get. So if you divide 1/infinity would that equal zero? And if that is true then would 1/0=infinity be true also? Answered by Penny Nom. 





Is a zero considered an even or odd number? 
20051213 

From Sylvia: Is a zero considered an even or odd number? Answered by Penny Nom. 





111111...111 divided by 3 
20051114 

From Jesus: If we divide the number 1111...........1( it has got 2004 digits) by 3. How many zeros will we get?. The answer that I have found in the book is 667 but I do not know how to reached it. Answered by Penny Nom. 





Why is zero even? 
20051108 

From Lauren: A child in my class if having trouble with the concept of zero being an even number, I have talked with her about its zero because it is a multiple of 2, any other suggestions? Answered by Paul Betts. 





'zero divided by one' and 'one divided by zero' 
20050131 

From Katrina: Please advise how best to explain the distinction between the solution to 'zero divided by one' and 'one divided by zero'. I remember being told in school that one of them is undefined and the other is zero but I'm having difficulty with calculating and explaining it to some highly curious 10 year olds! Answered by Claude Tardif and Walter Whiteley. 





Zero to the zero 
20040918 

From Greta: My name is Greta, and I am a 7th grader and my test is coming up. The question I would like to ask you is why 0 elevated to 0 is unidentified. Answered by Penny. 





112! 
20040528 

From Beatriz: 1) A bus driver collects identical sets of 5 coins from each passenger. If the totoal colledted was $21.83, how many pennies did the driver get??
2) How many terminal zero in the base 10 expression of 112! (factional) N! means N(N1)(N2) .....(2) (1). Answered by Penny Nom. 





The intersection of two graphs 
20040331 

From Benjanim: How do I find the points of intersection of the two functions:
1) y = 2  (e^x)
2) y = 1 + (x^2)
I know that I have to set them equal to each other, but I can't solve for x. Please help :) Answered by Penny Nom. 





Zero 
20040212 

From Syazwan: can you tell me who and when the number zero was
discoveredd Answered by Penny Nom. 





Dividing zero by infinity 
20040108 

From Jason: What do you get when dividing zero by infinity? Our Calculus teacher was pretty sure that the expression was indeterminate from. However, if this is so...Why? Zero divded by any number (except zero) is zero, true. Any number (except infinite) over infinite is zero. So, why isn't Zero divided by infinite zero. A simpler way if I had 4 potatoes and was to split them among 2 friends, each friend would get 2 potatoes. However, if I had 0 potatoes and split them a infinite number of ways, each person would still have 0. Explain please! Answered by Penny Nom. 





Is zero even? 
20040107 

From A secretary at an elementary school: Is zero an even number? Answered by Penny Nom. 





1/0 = ?? 
20031209 

From Lisa: One of my students asked me a fractions question. She knows that 0/1
equals 0 but does 1/0 also equal 0? Answered by Walter Whiteley and Penny Nom. 





0/0 
20030925 

From Thomas: How is 0/0 ever defined. Answered by Penny Nom. 





Positive, negative and zero 
20030904 

From Brian: Can the Value of zero be positive or can it be negative or can it be both. Answered by Penny Nom. 





Why is 5 to the 0 power always 1? 
20030824 

From Crystal: Why is 5 to the 0 power always 1? Answered by Penny Nom. 





Polynomials degree 4 and bigger 
20030626 

From Stephen:
How do I show kids how to find all the zeros for polynomials degree 4 and bigger.
For examples: r(x) = x^{5}11x^{3}7x^{2}+77 = (x^{2}11)(x^{3}7) and s(x) = x^{4}121 = (x^{2}11)(x^{2}+11) Also am I correct when I say that the following are irreducible? f(x) = x^{2}11 g(x) = x^{3}7 h(x) = x^{4}5 Answered by Harley Weston. 





(n+17)(n+7) = 0 
20030305 

From Janea:
What is the answer to 1. (n+17)(n+7)=0 What is the answer to:2. (y15)(y100)=0 Answered by Penny Nom. 





Division by zero 
20030119 

From David: I've been to your site and am interested on the subject of division by 0. It's easy enough to give answers, but it's very hard, especially in this case, to make someone understand a mathematical problem. It's been about a year since my Calc class, and we never went over division by 0, only infinite numbers and such. My question is: How would you work a problem of (real number) / 0 ? As ignorant as it may sound to you, I am having trouble grasping this since I've only begun to understand some of it. Perhaps you could help. Answered by Harley Weston. 





Three algebra problems 
20021013 

From Veronica: Solve the following inequality: 5(xsqured4)/(xto the 5th(2x5)to the 3rd) < or equal 0 Solve the following equations for all roots square root of x+2=1+square root of 2x+3 what's ZERO FACTOR PROPERTY??? The hypotenuse of an isosceles right triangle is 7cm. long. Determine the lenghts of the other sides. Answered by Leeanne Boehm. 





Exponent 0 
20021002 

From Debbi: can you please tell me what the exponent 0 is (i.e. 7^{0}) Answered by Penny Nom. 





Division by zero 
20020718 

From James: Why is division by zero undifined (i have to proof that division by zero is undifined) Answered by Chris Fisher. 





0/4 = ? 
20020428 

From Danielle: I am embarrased to be asking this question, but... is it possible to have a fraction with a zero? For example, 0/4. This does not make sense to me and I do not know what it would be representing, other than nothing! Is it proper to express such a fraction? Answered by Peny Nom. 





A polynomial 
20020414 

From A student: A polynomial function is described by the following conditions: f(x) has two real zeros at x= 2 and x= 1, each of multiplicity 2 f(x) has two complex zeros as x goes to infinity, f(x) goes to +infinity as x goes to +infinity, f(x) goes to +infinity f(x) has a yintercept at (0,2) Sketch a polynomial function that satisfies the above conditions. Write an equation for function f(x) Write another function g(x) that also satisfies the above parameters. Answered by Penny Nom. 





F = 3 + 3 
20020319 

From Jessica: F= 3 + 3 WHAT IS F????? Answered by Penny Nom. 





Negative numbers 
20011115 

From Jewel: If zero means nothing or an empty set, then how can a number be less than zero, as in negative number? My understanding of negative numbers is distance from a set point in a given direction. Thus having a negative and positive side of a line is arbritary and is related to displacement rather than value. Am I in error? Answered by Penny Nom. 





Division by zero 
20011031 

From Stacy: I have a question about dividing with zero. When the numerator is zero, the answer is zero. But when the denominator is zero, the answer is undefined. Why? I don't understand Answered by Claude Tardif. 





Zero as an exponent 
20011004 

From Wendy: How do I explain to kids that i.e. 5 exponent 0 = 1? Does 0 exponent 0 = 1? Answered by Leeanne Boehm and Penny Nom. 





Borrowing from zero 
20010330 

From Nikki: Here is the problem: 5,033.56  866.20 Now I know this equals 4,167.36 which I figured out on the calculator just to make sure. But when I did it by hand, I kept ending up with 5,167.36, which I knew was impossible. What am I doing wrong?? Answered by Leeanne Boehm and Claude Tardif. 





Why is 0! = 1? 
20010130 

From Diane: Every math book always claims that 1!=1 and 0!=1 are givens, and that we should just memorize it. i understand the 1! part, but where is the basis for claiming that 0!=1???? Answered by Walter Whiteley. 





10,000! 
20000721 

From Lauren: Hi I was just wondering if you could tell me how many zeros are in 100,000! (factorial.) Answered by Denis Hanson. 





How many zeros? 
20000409 

From Greg Potts: The natural numbers 1 to 25 are multiplied together (1 x 2 x 3x..24 x 25). How many zeros are there in the product of this multiplication? a)6 b)7 c)5 d)10 or e)4? Answered by Harley Weston. 





More on googols 
20000223 

From Kevin Brennan: Could you please give me a couple of examples of when you MATH guys would use a google. Do youu measure, like, galaxies with it ? Or was it created to keep track of Mr Gate's bank account. Answered by Penny Nom. 





Is zero an even or odd number? 
20000206 

From Christian Hansen: On a list I run, someone posted that 02022000 was the first date since 2808888 where all the digits were even. Of course, this provoked a discussion of whether zero was odd, or even, or neither. I remember reading that, for symmetry's sake, it is considered by mathematicians to be even. Any thoughts? Answered by Patrick Maidorn. 





zero 
20000101 

From Jason: What civilization first used zero? Answered by Penny Nom. 





Zero to the zero 
19991202 

From A middle school teacher: I am a middle school teacher who is looking for a precise explanation of why zero raised to the zero power is undefined. I am hoping to get an explanation using something other than the fact that diividing by zero is undefined. Answered by Penny Nom. 





Powers of zero 
19991031 

From Salina Young: Hello! I have two questions to ask about the power of "0". First, what is the value of "0' to the power of "0"? And why? Second, what is the value of "0" to the power of "2" or '3" etc? And why? Thank you for your help. Answered by Walter Whiteley and Harley Weston. 





A googol 
19991006 

From Kevin Brennan: describe to me a guegoll is that how u spell it? it sounds like that Answered by Penny Nom. 





Is zero positive? 
19990903 

From Shah: Is zero a positive integer? Answered by Penny Nom. 





Division by zero 
19990902 

From Joshua B. Mariano: Why can't I divide a number by zero. When I put in my calculater 0 divided by 7 it equals 0. But when I put 7 divided by zero my calculater say's error. Why can't this be solved? What is the answer? Is there a paper on it? Help? Answered by Walter Whiteley. 





Large Numbers 
19990405 

From CK: Hello. I need a lesson plan for grades 4 to 7 dealing with the concept of large numbers. Specifically, how to teach scientific notation. The lesson plan has to deal with the following: the size of the universe is so huge that is is almost beyond the ability of the mind to comprehend. One way is to measure... Answered by Chris Fisher. 





Finding Excluded Values 
19990401 

From Lorraine Le Cam: The question asks me to find the value of the variable that must be excluded in each rational expressionion. The operation is: a ______ a  2 How do I work this out? Answered by Harley Weston. 





0/11 
19990309 

From Jacob: What is the term applied to 0 divided by a number. In calculating slope problem my answer was 0 divided by 11. I don't know what to do with this answer or how to interpret it. Answered by Jack LeSage and Penny Nom. 





Indeterminate forms 
19981211 

From R. Dixon: What is the correct evaluation of infinity/0 ? I've checked three different math sites. One says definitively, that infinity/0 is "not" possible. Another states that infinity/0 is one of the indeterminate forms having a large range of different values. The last reasons that infinity/0 "is" equal to infinity. Answered by Walter Whiteley and Harley Weston. 





(4)^0 = ? 
19981202 

From Derek Yau: I would like to know why any number to the exponent 0 equals to 1 also, I would like you to please answer this question: (4)^0 = ? I know the answer is 1 but I am confused as to if it is a negative one or a positive one. Answered by Jack LeSage and Penny Nom. 





Social Security Numbers 
19980707 

From Valerie Lucas: How many social security numbers are possible? the answer is 10^9 why isn't the answer 9^9? Answered by Harley Weston. 





15 to the zero 
19980624 

From Mike Husken: My daughter has the problem: 15 with an exponent of zero=1. Could you help explain why? I would appreciate an answer soon as she has class tomorrow. thanks, Answered by Penny Nom and Patrick Maidorn. 





(50^20)(20^50) 
19980224 

From fion: 50 power of 20 X 20 power of 50? How many zero can be found in the answer and why? Answered by Penny Nom. 





0! 
19970302 

From Donna D. Hall: I am looking for a quick and easy explanation as to why 0! is 1. Answered by Walter Whiteley and Denis Hanson. 





Division by zero 
19970214 

From Linda Hood: I am a college student and have been asked to explain and figure out why we can't divide by zero. Answered by Chris Fisher. 





a to the power zero 
19960603 

From Beti: Why is a number to the power 0 equal to 1? Answered by Harley Weston. 





Cardano's method 
19960311 

From Mike Gorski: What is Cardano's method for finding the roots of a cubic equation? Answered by Harley Weston. 





Zero 
20010315 

From Alexandre: j'aimerais beaucoup savoir si le chiffre zéro est considéré comme étant soit:  pair
 impair
 pair et impair ŕ la fois
 ni pair ni impair.
Answered by Claude Tardif. 





Exposant ŕ la 0 
20000704 

From Sylvie: J'aimerais savoir combien fait 0 exposant 0. Answered by Claude Tardif. 

