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Find all integers $n$ such that the quadratic $7x^2 + nx - 11$ can be expressed as the product of two linear factors with integer coefficients.

 Dec 18, 2019
 #1
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7x^2  + nx  - 11

 

7 and 11 are prime....so the possible factorizations are

 

(7x + 11) ( x + 1)   ⇒   n =  18

 

(7x + 1) (x + 11)   ⇒  n = 78

 

(-7x + 1)(-x + 11)  ⇒ n = -78

 

(7x - 11)  ( x - 1) ⇒  n = -18

 

 

 

cool cool cool

 Dec 18, 2019
 #2
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I'm a little confused, doesn't the first one turn into (7x+11)(x+1)=7x^2+7x+11x+11=7x^2+18x+11 instead of -11

 Dec 19, 2019

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