Question

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

Answer 1

Bro there is a mistake in the question. I think the the factor should be (x +a)


Sub. x = -a on both the polynomials.

Answer 2

Ello user !!!!!

Here is your answer,

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Substitute x with a

(-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 

a=n-q/m-p

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HOPE THIS HELPS YOUU :)

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