Let $\alpha, \beta$ be the roots of $x^2 - x + p = 0$ and $\gamma, \delta$ be the roots of $x^2 - 4x + q = 0$ where p and q are integers. If $\alpha, \beta, \gamma, \delta$ are in…

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Let $\alpha, \beta$ be the roots of $x^2 - x + p = 0$ and $\gamma, \delta$ be the roots of $x^2 - 4x + q = 0$ where p and q are integers. If $\alpha, \beta, \gamma, \delta$ are in geometric progression then $p + q$ is

Accepted Answer

A - -34. Let terms be t, tr, tr^2, tr^3: t(1+r) = 1 and tr^2(1+r) = 4 so r = +-2. r = 2 gives p = 2/9 (not integer); r = -2 gives t = -1, p = t^2 r = -2, q = t^2 r^5 = -32, p+q = -34.

Answer

B - 30

Answer

C - 26

Answer

D - -38

Let \(\alpha, \beta\) be the roots of \(x^2 - x + p = 0\) and \(\gamma, \delta\) be the roots of \(x^2 - 4x + q = 0\) where p and q are integers. If \(\alpha, \beta, \gamma, \delta\) are in…

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