Math CentralQuandaries & Queries


Question from Nazrul, a teacher:

If x+a be the h.c.f. of x2+px+q and x2+mx+n, how can I prove that (p-m)a=q-n.

Hi Nazrul,

We have two responses for you:

First Response

If x+a is a common factor ("highest" is meaningless here) of x2+px+q and x2+mx+n, then there exist b,c such that

(x+a)(x+b) = x2+px+q
(x+a)(x+c) = x2+mx+n

Good Hunting!

Second Response

The Remainder Theorem states if x+a is a factor of f(x)= x2+px+q then

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

Hope this hint helps,


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