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

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

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    $\begingroup$ The gcd $x+a$ must divide their difference $\endgroup$ – Bill Dubuque May 13 at 20:52
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hint

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

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