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MathNet 2016-part-05 — 184 problems (EN–VI) Question 65

Math Olympiad Vault · MathNet 2016-part-05 — 184 problems (EN–VI)

Question 65

The quadratic equations $x^{2} + a x + 2 = 0$ and $x^{2} + 2 x + a = 0$, where $a$ is a real number, have real solutions. The sum of the squares of the solutions of the first equation equals the sum of the squares of the solutions of the second equation. What is $a$?

(A) $-4$
(B) $-2$
(C) $0$
(D) $4$
(E) None of the above.