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Quadratic Equations

If the roots ...

Question

If the roots of the equation $2 x^{2} - 3 x + 5 = 0$ are reciprocals of the roots of the equation $a x^{2} + b x + 2 = 0$ , then

a = 2, b = 3

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a = 2, b = - 3

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a = 5, b = - 3

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a = 5, b = 3

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Solution

The correct option is B $a = 5, b = - 3$
Let $α, β$ are roots of $2 x^{2} - 3 x + 5 = 0$
Then to get equation whose roots are $\frac{1}{α}, \frac{1}{β}$
Replace $x \to \frac{1}{x}$
We get $5 x^{2} - 3 x + 2 = 0$ .

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