Find two integers whose product is -12 and whose sum -11.

Question

My question is under quadratic equations section of my book. 

Answer 1

The sum of 2 integer is the middle term of a quadratic expression.  The product of the same 2 integers is the last term of the quadratic expression.  So our quadratic expression is

 

x² - 11x - 12

 

 

This can be factored as

 

x² + (r + q)x + rq

 

(x + r)(x + q)

 

(x - 12)(x + 1)

 

 

where  r and q are the two 2 integers.  The two integers are then -12 and 1.