If the roots of $x^{5} - 40 x^{4} + P x^{3} + Q x^{2} + R x + S = 0$ are in G.P. and the sum of their reciprocals is $10$ , then $| S |$ is equal to

4

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6

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8

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none of these

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Solution

The correct option is C none of these
$S u p p o s e t h e r o o t s a r e \frac{a}{r^{2}}, \frac{a}{r}, a, a r, a r^{2} S o S = a^{5} a n d \frac{a}{r^{2}} + \frac{a}{r} + a + a r + a r^{2} = 40 S u m o f r e c i p r o c a l s a r e 10 \frac{1}{a} (\frac{40}{a}) = 10 a = \pm 2 S o | S | = 32$

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Similar questions

x^{5} - 40 x^{4} + P x^{3} + Q x^{2} + R x + S = 0

10

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