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Discriminant

If α,β are th...

Question

If $α, β$ are the roots of the equation $2 x^{2} - 35 x + 2 = 0$ , then the value of $(2 α - 35)^{2} (2 β - 35)^{2}$ is

A

16

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B

8

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C

64

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D

None of these

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Solution

The correct option is A $16$
$α + β = \frac{35}{2}, α β = 1 \Rightarrow - 2 β = (2 α - 35), - 2 α = (2 β - 35) \Rightarrow 4 α β = (2 α - 35) (2 β - 35) \Rightarrow (2 α - 35)^{2} (2 β - 35)^{2} = 16 (α β)^{2} ∴ (2 α - 35)^{2} (2 β - 35)^{2} = 16$

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