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All the roots of

x^2 + px + q = 0
are real, where p and q are real numbers. Prove that all the roots of

x^2 + px + q + (x + a)(2x + p) = 0
are real, for any real number a. 

 Jan 17, 2021
 #1
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Since x^2 + px + q has real roots and (x + a)(2x + p) has real roots, x^2 + px + q + (x + a)(2x + p) also has real roots.

 Jan 17, 2021

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