The quadratic equation whose roots are three | vedclass

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Question

(A) Let the roots of the given equation $3ax^2+3bx+c=0$ be $\alpha$ and $\beta$.Then,$3a\alpha^2+3b\alpha+c=0$.We want to find the equation whose root

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$ax^2+3bx+3c=0$

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(A) Let the roots of the given equation $3ax^2+3bx+c=0$ be $\alpha$ and $\beta$.Then,$3a\alpha^2+3b\alpha+c=0$.We want to find the equation whose roots are $3\alpha$ and $3\beta$. Let $x = 3\alpha$,which implies $\alpha = \frac{x}{3}$.Substituting $\alpha = \frac{x}{3}$ into the original equation:$3a(\frac{x}{3})^2 + 3b(\frac{x}{3}) + c = 0$$3a(\frac{x^2}{9}) + bx + c = 0$$\frac{ax^2}{3} + bx + c = 0$Multiplying the entire equation by $3$,we get:$ax^2 + 3bx + 3c = 0$.

The quadratic equation whose roots are three times the roots of $3ax^2+3bx+c=0$ is

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