# Let (x+a) be the HCF of $x^2+px+q$ and $x^2+mx+n$. Show that $a=(q-n)/(p-m)$ [closed]

Let $$(x+a)$$ be the HCF of $$x^2+px+q$$ and $$x^2+mx+n$$. Show that $$a=(q-n)/(p-m)$$.

## closed as off-topic by Xander Henderson, steven gregory, Leucippus, YiFan, John OmielanMay 14 at 1:50

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• The gcd $x+a$ must divide their difference – Bill Dubuque May 13 at 20:52

## 1 Answer

hint

$$x+a$$ divides both polynomials. Hence $$x=-a$$ is a common root for both. Plug in $$x=-a$$ in both and subtract.