Question

If (x+a) is a factor of two polynomials x2+px+q and x2+mx+n, then prove that : a=n- q/m-p

Answer 1

(-a)² + p·(-a) + q = 0 --> a² -ap + q = 0 
(-a)² + m·(-a) + n = 0 --> a² -am + n = 0 
Since they both equal 0, you can set them equal to each other: 
a² -ap + q = a² -am + n 
-ap + q + -am + n 
am - ap = n-q 
a(m-p) = n-q 

Answer 2

Here ,

Firstly we have to obtain the zero from the given factor , i.e. (x+a).

The required zero = -a

Then we are given with two polynomials and the factor given is for both.

Put x = -a in both the polynomials.

And then they are equal to zero. So both of them are equal to each other. (According to Euclid's Postulate - Things equal to equals are equal to each other).

Then for the full solution refer to the above attachment.