Quandaries and Queries
  

 

Janea is my name. Im in the 10th grade and i'm a student.

What is the answer to 1. (n+17)(n+7)=0

What is the answer to:2. (y-15)(y-100)=0

 

 

Hi Janea,

The number zero has a very special property that is useful here. Suppose I tell you that I have two numbers p and q and that pq = 12. There are many choices for p and q. They might be 2 and 6 or 3 and 4 or 1 and 12 or many other choices if you allow fractions. If however I tell you that I have two numbers p and q and that pq = 0 then you have much more information. If pq = 0 then either p = 0 or q = 0 or perhaps both p and q are zero.

Thus for question 1, since (n+17)(n+7) = 0 you know that

  1. n + 17 = 0 or

  2. n + 7 = 0, or

  3. n + 17 = 0 and n + 7 = 0
That is
  1. n = -17 or

  2. n = -7, or

  3. n = -17 and n = -7
Clearly the third option is impossible so you know that n is either -17 or -7.

Cheers,
Penny 		 
 

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