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Question

If α,β are roots of the equation 2x2-35x+2=0, then the value of (2α-35)3×(2β-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 C

64


Explanation of the correct answer:

α,β are roots of the equation 2x2-35x+2=0

Sum of roots (α+β)=-ba=352

Product of roots (αβ)=ca=1

When α is a root

f(α)=2α2-35α+2=0f(α)=2α-35=-2α

When β is a root

f(β)=2β2-35β+2=0....(i)f(β)=2β-35=-2β....(ii)

Putting (i) and (ii) in (2α-35)3×(2β-35)3

(2α-35)3×(2β-35)3=(-2α)3×(-2β)3=64αβ=641=64

Hence, option (C) is correct.


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