If the roots of $x^{4} + 5 x^{3} - 30 x^{2} - 40 x + 64 = 0$ are in G.P. then the roots are

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1, –2, 4, –8

$\pm 1, 2, 3$

$\pm 2 i, 2, 3$

$\frac{3}{2}, - \frac{1}{3}, 2 \pm \sqrt{3}$

answer is A.

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Detailed Solution

$\begin{array}{l} L e t \frac{a}{r^{3}}, \frac{a}{r}, a r, a r^{3} a r e r o o t s o f x^{4} + 5 x^{3} - 30 x^{2} - 40 x + 64 = 0 \\ ∴ \frac{a}{r^{3}} . \frac{a}{r} . a r . a r^{3} = 64 \\ \Rightarrow a^{4} = 64 \end{array}$

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