If alpha, beta are the roots of a x^2+b x+c=0 | vedclass

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(A) Given that $\alpha$ and $\beta$ are the roots of $a x^2+b x+c=0$. Let the roots of the new equation be $t = \sqrt{5} \alpha$ and $t = \sqrt{5} \be

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$a x^2+\sqrt{5} b x+5 c=0$

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(A) Given that $\alpha$ and $\beta$ are the roots of $a x^2+b x+c=0$. Let the roots of the new equation be $t = \sqrt{5} \alpha$ and $t = \sqrt{5} \beta$. Then $\alpha = \frac{t}{\sqrt{5}}$. Substituting this into the original equation: $a(\frac{t}{\sqrt{5}})^2 + b(\frac{t}{\sqrt{5}}) + c = 0$ $\frac{a t^2}{5} + \frac{b t}{\sqrt{5}} + c = 0$ Multiplying the entire equation by $5$: $a t^2 + 5 \frac{b t}{\sqrt{5}} + 5 c = 0$ $a t^2 + \sqrt{5} b t + 5 c = 0$ Replacing $t$ with $x$,the required equation is $a x^2 + \sqrt{5} b x + 5 c = 0$.

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

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