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Question

If $$\alpha,\beta$$ are roots of the equation $$2x^2-35x+2=0$$ then the value of $$(2\alpha-35)^3(2\beta-35)^3$$ is:


A
1
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B
8
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C
4
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D
64
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Solution

The correct option is C $$64$$
We will substitute $$\alpha, \beta $$ in the above equation

$$\Rightarrow 2\alpha - 35+\dfrac {2}{\alpha} =0$$

$$\Rightarrow 2\alpha - 35=\dfrac {-2}{\alpha} $$

Similarly for beta 

$$\Rightarrow (2\alpha - 35)^{3}(2\beta - 35)^{3}=\dfrac {-8}{\alpha ^{3}}×\dfrac {-8}{\beta^{3}}=\dfrac {64}{1}=64$$

Mathematics

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