jee-main 2024 Q61

jee-main · India · session1_01feb_shift2 Geometric Sequences and Series Arithmetic-Geometric Sequence Interplay

Let $\alpha$ and $\beta$ be the roots of the equation $px^2 + qx - r = 0$, where $p \neq 0$. If $p, q$ and $r$ be the consecutive terms of a non-constant G.P and $\frac{1}{\alpha} + \frac{1}{\beta} = \frac{3}{4}$, then the value of $\alpha - \beta^2$ is:
(1) $\frac{80}{9}$
(2) 9
(3) $\frac{20}{3}$
(4) 8

Let $\alpha$ and $\beta$ be the roots of the equation $px^2 + qx - r = 0$, where $p \neq 0$. If $p, q$ and $r$ be the consecutive terms of a non-constant G.P and $\frac{1}{\alpha} + \frac{1}{\beta} = \frac{3}{4}$, then the value of $\alpha - \beta^2$ is:\\
(1) $\frac{80}{9}$\\
(2) 9\\
(3) $\frac{20}{3}$\\
(4) 8

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