iran-konkur 2021 Q101

iran-konkur · Other · konkur-riazi_1400_specialized Roots of polynomials Vieta's formulas: compute symmetric functions of roots
101- If the sum and product of the real roots of the equation $x^4 - 7x^2 - 5 = 0$ are $S$ and $P$ respectively, what is the value of $2P^2 - 3SP + 2S$?
(1) $59 - 7\sqrt{69}$ (2) $7 + \sqrt{69}$ (3) $50$ (4) $59 + 7\sqrt{69}$
\textbf{101-} If the sum and product of the real roots of the equation $x^4 - 7x^2 - 5 = 0$ are $S$ and $P$ respectively, what is the value of $2P^2 - 3SP + 2S$?

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(1) $59 - 7\sqrt{69}$ \hfill (2) $7 + \sqrt{69}$ \hfill (3) $50$ \hfill (4) $59 + 7\sqrt{69}$

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