Question

Please solve this question.​

Answer 1

If x+a is a factor:

x = -a

Put this in p(x) = x^2 + px + q and p(x') = x^2 + mx + n

p(-a) = (-a)^2 + p(-a) + q = 0

=> a^2 - ap + q = 0

p(-a) = (-a)^2 + m(-a) + n = 0

=> a^2 - am + n = 0

Equate the bole equations:- [Since both of them are equal to zero]

=> a^2 - ap + q = a^2 - am + n

=> am - ap = n - q

=> a = (n - q)/(m - p)

hence proved.