If $\alpha, \beta$ are the roots of $a x^2+b x+c=0$, then the quadratic equation whose roots are $\sqrt{5} \alpha, \sqrt{5} \beta$ is

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Aicharya · Accepted Answer

$\alpha$ and $\beta$ are roots of $a x^2+b x+c=0$ Consider $\sqrt{5} \alpha=t \Rightarrow \alpha=\frac{t}{\sqrt{5}}$ $ \begin{aligned} & 	herefore a\left(\frac{t}{\sqrt{5}}ight)^2+b\left(\frac{t}{\sqrt{5}}ight)+c=0 \ & \Rightarrow \quad \frac{a t^2}{5}+\frac{b t}{\sqrt{5}}+c=0 \Rightarrow a t^2+b \sqrt{5} t+5 c=0 \end{aligned} $ $	herefore$ Equation whose roots are $\sqrt{5} \alpha, \sqrt{5} \beta$ is $ a x^2+b \sqrt{5} x+5 c=0 $

If $\alpha, \beta$ are the roots of $a x^2+b x+c=0$, then the quadratic equation whose roots are $\sqrt{5}…

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