The quadratic equation whose roots are twice the roots of 2x2 - 5x + 2 = 0 is

Question

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

Smart Achievers · Accepted Answer

(2)

$Quadratic equation is 2 x^{2} - 5 x + 2 = 0$

Let $α$ and $β$ are its roots.

$∴$ $α + β = \frac{5}{2},$ $α β = 1$

Now roots of another equation are $α' = 2 α$ and $β' = 2 β$

$α' + β' = 2 α + 2 β = 2 (α + β) = 5$

$α' β' = 2 α \times 2 β = 4 α β = 4$

Now quadratic equation with roots $α'$ and $β'$ is

$x^{2} - (α' + β') x + α' β' = 0$ $\Rightarrow x^{2} - 5 x + 4 = 0$

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