jee-main 2020 Q52

jee-main · India · session2_04sep_shift1 Roots of polynomials Vieta's formulas: compute symmetric functions of roots

Let $\alpha$ and $\beta$ be the roots of $x ^ { 2 } - 3 x + p = 0$ and $\gamma$ and $\delta$ be the roots of $x ^ { 2 } - 6 x + q = 0$. If $\alpha , \beta , \gamma , \delta$ from a geometric progression. Then ratio $( 2 q + p ) : ( 2 q - p )$ is
(1) $3 : 1$
(2) $9 : 7$
(3) $5 : 3$
(4) $33 : 31$

Let $\alpha$ and $\beta$ be the roots of $x ^ { 2 } - 3 x + p = 0$ and $\gamma$ and $\delta$ be the roots of $x ^ { 2 } - 6 x + q = 0$. If $\alpha , \beta , \gamma , \delta$ from a geometric progression. Then ratio $( 2 q + p ) : ( 2 q - p )$ is\\
(1) $3 : 1$\\
(2) $9 : 7$\\
(3) $5 : 3$\\
(4) $33 : 31$

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