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Let  $p$ and $q$ be real numbers such that the roots of

\[x^2 + px + q = 0\]

are real. Prove that the roots of

\[x^2 + px + q + (x + a)(2x + p) = 0\]
are real, for any real number $a$

 Jun 29, 2020
 #1
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You know that x^2 + px + q = 0, so you just have to show that (x + a)(2x + p) = 0.

 Jun 29, 2020

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