







Quadratic Equations 
20170328 

From Natalie:
Hi Maths Central,
I am having trouble with quadratic equations. The question is:
Calculate the length 'l' of a rectangular pool by creating and solving a quadratic equation.
1. The rectangular pool is of equal area to a square pool, and a circular pool (5.70m^2).
2. The length of the rectangular pool must be 2m longer than the width 'w'.
Thank you so, so much for your help, Maths Central! Answered by Penny Nom. 





Solve 3x^219x14=0 for x 
20170315 

From nick: I'm an 8th grader and am quite confused with this equation:
3x^219x14=0
The answer is:
2/3 , 7
But I'm not sure how to solve for it. Answered by Penny Nom. 





Form the quadratic equation which has given roots 
20170116 

From Tharshini: Given a and B are the roots of the quadratic equation x^2+4x+7=0. Form the quadratic equation which has the roots
3a1 and 3B1 Answered by Penny Nom. 





Solve 2^2x + 3(2^x)  4 = 0 
20160427 

From Lloyd: Solve the equation 2^2x + 3(2^x)  4 = 0 Answered by Penny Nom. 





A quadratic equation with equal roots 
20160123 

From abdiwahid: X^2+2ax+4x+9a=0 is quadratic equation which has equal roots. Find the possible value of a? Answered by Penny Nom. 





Find the quadratic equation whose roots are 4 and 7 
20160103 

From sadiya: Find the quadratic equation whose roots are 4 and 7 Answered by Penny Nom. 





A quadratic equation with known roots 
20151101 

From Awudu: Given the roots of the quadratic equation ax^2+5x+c=0 are 5 and 2/3,find the values of a,b and c. Answered by Penny Nom. 





2p^2+4p=16. How do i get p? 
20150922 

From Dohie: How do i solve this?
2p^2+4p=16. How do i get p?
Thanks Answered by Penny Nom. 





Two consecutive positive integers 
20150301 

From meha: Find two consecutive positive integers , sum of whose squares is 365. Answered by Penny Nom. 





Two quadratic equations 
20141120 

From rajesh: Sir,
I would like to discuss on question
Find the value of variable X and Y, equations are
X2+Y2+2XY=25
X2+Y22XY=1
Sir, my point is equation looks not so easy.My opinion is there many
(more than 4)value possible for both X and Y.
Kindly help me.
Waiting for your response.
regards,
rajesh Answered by Penny Nom. 





A quarter mile row of trees 
20141009 

From junna: a farmer would like to plant trees on one side
of his lot which is 1/4 of a mile in a length
His friend advised him that if he would plant
the trees 5 feet farther apart,he would need 44
fewer trees.If the farmer would take the advice,
how many trees would he plant? Answered by Penny Nom. 





A quadratic equation 
20140920 

From Najah: (E): (m2_1)x2 _ (m+3)x+4_m2=0
A) for what values of m is the equation (E) quadratic?
B) for what value of m is the real number 1 a root of (E) Answered by Penny Nom. 





A quadratic equation given the roots 
20140423 

From Sarah: How do you find the quadratic formula when you're given just the roots ... X=3 X= 1/3
Thanks ! Answered by Robert Dawson. 





A quadratic equation 
20131127 

From corinanna: Hi,
How do you find a quadratic equation given the domain & range,
& or the yintercept? Answered by Penny Nom. 





Solve 0=2(x5)^2+4 
20131117 

From Leila: How do you find the solution to 0=2(x5)^2+4 Answered by Penny Nom. 





A quadratic with no real roots 
20130715 

From Pranav: If ax^2+bx5=0 has no real roots. Then d sign of 1) a+b5
2) (25a5b5)(4a+2b5) will be what ?? Answered by Penny Nom. 





Two quadratic equations 
20121122 

From fahmie: graph and solve the intersection of the following equations:
x^2+y^2=4
x^2+2y=4 Answered by Penny Nom. 





A quadratic function 
20120608 

From Salehah: Hi there, i dont know how to do quadratic equations. So how do i do the question,
that says: xint 4 and 2, and yint of 4? and we are to maek a quadratic function with this information.
Please help!
Thank you very much!
Salehah Answered by Robert Dawson. 





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. 





Three consecutive numbers 
20111129 

From Michael: Find three consecutive numbers such that the second number squared
is equal to the first and third added together Answered by Penny Nom. 





A picture with a frame 
20110819 

From Aniish: A picture 8inches by 12inches is placed in a frame of uniform width. If the area of the frame equals the area of the picture find the width of the frame? Answered by Penny Nom. 





Throwing a football 
20110208 

From Janet: a football is thrown into the air from 2 meters high. After 1 second it is 6.9 meters high. After another second it is 2 meters high. How high is it after 1.02 seconds and .05 seconds? when will it reach 5.136 meters? I am not sure how to extract the numbers I need and what equations to use them in? Answered by Stephen La Rocque. 





The suspension cables of a bridge 
20100729 

From Mike: what is the formula for the suspension cables of a bridge.
The towers are 200 ft above the roadway
The towers are 3400 ft apart
The cable if at 8ft in the middle of the span Answered by Robert Dawson. 





A quadratic equation with imaginary numbers 
20100603 

From Alissa: I am solving a quadratic equation and I got this far;
(x4+i)(x4i)=0
but how do I add the imaginary numbers
i know you multiply x by x and then add 4 + 4 but what do you do with the i's? Answered by Penny Nom. 





The product of two consecutive even integers 
20100511 

From Terry: The product of two consecutive even integers is 14 more than their sum. Find the integers. Answered by Penny Nom. 





A quadratic equation 
20100503 

From Millie: (3x4)(5xplus2)=0 Answered by Penny Nom. 





A piece of string 8 inches long is cut in two pieces 
20100202 

From Susan: If you have a piece of string 8 inches long and cut it in two pieces. Then take the pieces and forms
each into a square such that the area of each squares added together equals 2. How long are the
sides of the squares?
Susan Answered by Penny Nom. 





Quadratic equations 
20090830 

From jovian: how can i find the quadratic equation of the roots 2/5 and 1/3? Answered by Stephen La Rocque. 





Factoring 
20090823 

From Bj: Solve for x: 5x^2  35x = 0 Answered by Stephen La Rocque. 





4cos^2 (3x) + 3sin (3x) = 1 
20090505 

From Cheryl: Find all solutions of the following equation and show how to do this algebraically.
4cos^2 (3x) + 3sin (3x) = 1 Answered by Harley Weston. 





A quadratic equation with roots (4i) and (4+i) 
20090505 

From Kelly: find a quadratic equation with roots (4i) and (4+i) Answered by Harley Weston. 





cos2x = sinx 
20090419 

From stacey: solve the equation cos2x = sinx for 0 < x < 2 pi
giving the answer in terms of pi. Answered by Harley Weston. 





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. 





Quadratic equations arising from practical problems 
20081124 

From Lenval: Why do quadratic equations arising from practical problems often give physically impossible solutions such as negative distances, negative times or, say, a polygon with a negative number of sides? For example: "A river in flood carries a tree tsquared  23t metres downstream in t seconds. How long does it take for the tree to be carried 50 metres downstream?" This gives t=25 and t=2. Please explain the second 'solution', which is not physically possible. Answered by Chris Fisher and Victoria West. 





Solving an Equation with a Square Root 
20081005 

From Jonathan: the square root of 3x+18 = x
3x+18 are within the square root Answered by Victoria West. 





cos^2x  3cosx = 1 
20080929 

From Danielle: cos2x  3cosx = 1 Answered by Penny Nom. 





y^2+3yz8z4z=0 
20080817 

From Rae: y^2+3yz8z4z=0 Answered by Penny Nom. 





algebra 
20080731 

From Eric: Would you please solve & explain this equation to me: x^2+2x=x(x+2)?
Thank you Answered by Penny Nom & Stephen La Rocque. 





Width of a Garden Path 
20080730 

From Erin: A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet? Answered by Janice Cotcher. 





3y^2  48 = 0 
20080623 

From marquis: 3y^2  48 = 0 Answered by Stephen La Rocque. 





A quadratic equation 
20080603 

From Drew: A solution of x^28x=17 is
4 or 4+I or 4 or 4+i Answered by Janice Cotcher. 





Find the quadratic equation with roots at (3i) and its complex conjugate 
20080422 

From Tiffany: Find the quadratic equation with roots at (3i) and its complex conjugate. Answered by Penny Nom. 





A quadratic equation with odd coefficients 
20080415 

From Manashi: If p,q,r be any odd integers, then prove that the roots of the quadratic equation px^2+qx+r=0 can't be rational . Answered by Stephen La Rocque. 





A rectangle word problem 
20080410 

From Nick: A rectangle is twice as long as it is wide. If the length and width are both increased by 5cm, the resulting rectangle has an area of 50cm^2. Find the dimensions of the original. Answered by Penny Nom. 





Problems solved using quadratic equations 
20071007 

From Lisa: a. Two positive numbers differ by 5. Their product is 234. What are the two numbers?
b. The sum of two numbers is 12. Their product is 30. What are the two numbers?
c.Two numbers differ by 5. Their squares differ by 55. What are the two numbers?
d. The sum of two numbers is 15. Their product is 56. By forming an equation, find the two numbers. Answered by Penny Nom. 





Can you solve this by factoring? 10r^2  35r = 10 
20070812 

From Aranxa: how do u solve this equation by factoring:
10r^2  35r = 10 Answered by Stephen La Rocque. 





15 = 19.2 t (time)  4.9 t squared 
20070611 

From Nicole: 15 = 19.2 t (time)  4.9 t squared Answered by Penny Nom. 





Solving a quadratic equation using the Quadratic Formula 
20070605 

From Stuart: Solve the following quadratic equation:
3xsquared5x4=0 Answered by Stephen La Rocque. 





Intersection of a line and a circle 
20070412 

From gaby: The sum of two numbers is 9. The sum of the squares of the two numbers is 41. Find the numbers. Answered by Steve La Rocque and Melanie Tyrer. 





Fencing a field 
20070201 

From Carol: "The area of a rectangular field is 1200m^2. Two parallel sides are fenced with aluminum at $20/m. The remaining two sides are fenced with steel at $10/m. The total cost of the fencing is $2200." What is the length of each side fenced with aluminum and steel? Answered by Stephen La Rocque. 





A quuadratic equation 
20061222 

From Harold: L=3w4 A=96Square I used the quadratic equation to solve and my answer is still wrong
I convert the square of 1168 to decimal.
here is where i start (3w4) x w=96
could you give me an example Answered by Stephen La Rocque. 





The roots of a quadratic equation 
20061116 

From Lana: If p and q are the roots of 2X^2 +3X+7=0, compute pq^3+qp^3. thanks for your help. Answered by Penny Nom. 





Is this unsolvable? 
20060919 

From Al: Is this unsolvable???
2xy + 3x^2  3y + y^3 = 4x + 3 where y=3. Answered by Penny Nom and Claude Tardif. 





cos 2x = sin x 
20050122 

From Kris: solve the equation
cos 2x = sin x for 0<= x < 360 Answered by Penny Nom. 





x^2 = x + 2 
20040726 

From A parent: x2 = x+2
My daughter came home with this equation today and although I know the answer is x=2, i have no way of proving it by showing any working out. Answered by Penny Nom. 





Solving some quadratic equations 
20040715 

From A student: Could you please solve the following for x
x^{2}+6=5x
x^{2}+16=8x
2x+21=3x^{2} Answered by Penny Nom. 





The product of the page numbers 
20031107 

From Morgan and Mom: You open a book and the product of the page numbers is 12,656. What are your page numbers? Answered by Penny Nom. 





x6square root of x +8=0 
20030510 

From Elizabeth: x6square root of x +8=0 Answered by Penny Nom. 





Why quadratic? 
20030121 

From Dan: Why are equations of the form aX^{2} + bX + c =0 call quadratic? The quad indicates 4 but the power is 2. Answered by Penny Nom. 





Quadratic equations 
20021210 

From Katie: just bugging the hell outta me and I cannot figure it out for the life of me.
1)x2x1 =0 Find both roots. You must simplify both of your roots. This equation requires the use of the Quadratic Formula. I have tried everything for this and I am still either getting the wrong answers, and end up getting really frustrated. If you could find the answers and tell me how you did it I would greatly appreciate it! Then the second problem is
2) The square of a certain negative number is equal to 70 decreased by 3 times the number. Find the answer! On this one I set it up but still came out with the wrong answer. So if you could help me on this one I would greatly appreciate it! Answered by Penny Nom. 





A complex quadratic 
20021006 

From Michael: I would like to know, how to solve this Complex number: quadratic equation. ix^{ 2} + x i = 0 Answered by Harley Weston. 





A rightangled triangle 
20011213 

From Pamela, Jeff, Kayleigh and Jacob: A rightangled triangle has one side that is 8 cm shorter that the hypotenuse. The other side is 1 cm shorter than the hypotenuse. Find the length of the sides. Answered by Penny nom. 





Quadratic equations 
20010311 

From Philip: I am a student in the UK and i am in secondary school and i am doing my GCSE next year. here are my questions: solve the following equations correct to 2 decimal each time. [1] 2xsquared + 5x = 1 [2] 3xsquared(2x+1)=1 [3] xsquared + 7x + 2 = 2x + 4 [4] 5xsquared  3x = xsquared + 4 Answered by Penny Nom. 





Finding a Quadratic Equation given the roots 
20000416 

From A secondary student: How do I find the equation for the quadratic with roots at 2i and its complex conjugate? Answered by Harley Weston. 





Quadratic 
20000126 

From Karen Johnson: What is the reasoning behind the title quadratic equation? Answered by Penny Nom. 





Derive the quadratic equation 
20000101 

From Thuy: My teacher asked us this question in which i can't understand when she asked to derive the quadratic equation. What does this mean? Answered by Penny Nom. 





A ladder problem 
19990422 

From Michael Blade: There is a cube box 3feet x 3feet x 3ft resting against a vertical wall on level ground. Resting against the outside corner of the box is a ladder 10 feet tall, this ladder is of course resting on the ground but also against the outside corner of the box and rests on the wall. The question the ladder is divided into two unequal section bounded by the box to the ground and the box to the wall. what are those dimensions? Answered by Penny Nom. 





Quadratic equations 
19990331 

From Ken Niebergall: #1 a^{2}  10a = 2a  36 #2 t(t  5) = 5 (t  5) #3. (x + 4)(x  3) = 8 Thanks. Answered by Jack LeSage and Penny Nom. 





An airplane problem 
19990308 

From B.M.R.: A plane left New York and headed East to its destination 3600 miles away across the Atlantic. On the way back its speed was boosted by a 50 mph tail wind and it arrived an hour early. What was its normal speed? Answered by Jack LeSage. 





Find the Numbers. 
19971228 

From Sandy C: The sum of the squares of two numbers is 53. Twice the greater, minus the lesser is 11. Find the numbers. Answered by Penny Nom. 





Why QUADratic? 
19970319 

From Paula Miller: A student today asked me why a quadratic, with highest power of degree 2, was called a QUADratic. We're awaiting the answer with baited breath! :) Answered by Chris Fisher and Walter Whiteley. 

