The quadratic equation whose roots are twice the roots of $2 x^{2} - 5 x + 2 = 0$ is:

8 x^{2} - 10 x + 2 = 0

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x^{2} - 5 x + 4 = 0

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2 x^{2} - 5 x + 2 = 0

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x^{2} - 10 x + 6 = 0

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Solution

The correct option is B $x^{2} - 5 x + 4 = 0$
$\begin{matrix} L e t α a n d β b e t h e r o o t o f t h e g i v e n e q u a t i o n . T h e n, α + β = \frac{5}{2} a n d α β = \frac{2}{2} = 1 ∴ 2 α + 2 β ∴ (α + β) ∴ 5 (2 α) (2 β) = 4 S o t h e r e q u i r e d e q u a t i o n i s : x^{2} - 5 x + 4 = 0 \end{matrix}$

So, option $B$ is correct answer.

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Find the equation whose roots are reciprocals of the roots of $2 x^{2} + 5 x + 4 = 0$ .

2 x^{2} - 5 x - 3 = 0

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