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Geometric Progression

If a,b are ...

Question

If $a, b$ are roots of the equation $2 x^{2} - 35 x + 2 = 0$ , then the value of $(2 a - 35)^{3} . (2 b - 35)^{3}$ is equal to-

A

10

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B

100

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C

64

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D

1

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Solution

The correct option is D $64$
$f (x) = {2 x}^{2} - 35 x + 2 = 0 h a s r o o t s a & b p r o d u c t o f r o o t s = a b = \frac{2}{2} = 1 f (a) = 0 {2 a}^{2} - 35 a + 2 = 0 (2 a - 35) = \frac{- 2}{a} f (b) = 0 {2 b}^{2} - 35 b + 2 = 0 (2 b - 35) = - \frac{2}{b} {(2 a - 35)}^{3} . {(2 b - 35)}^{3} = {(\frac{- 2}{a})}^{3} {(\frac{- 2}{b})}^{3} = \frac{2^{6}}{{(a b)}^{3}} = \frac{2^{6}}{1} = 64$

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