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
B
8
C
4
D
64

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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