If the ratio of the roots of the equation px^ | vedclass

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(B) Let the roots of the equation $px^2+qx+r=0$ be $a\alpha$ and $b\alpha$. From the relation between roots and coefficients: Sum of roots: $a\alpha +

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$\frac{pr}{q^2}$

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(B) Let the roots of the equation $px^2+qx+r=0$ be $a\alpha$ and $b\alpha$. From the relation between roots and coefficients: Sum of roots: $a\alpha + b\alpha = (a+b)\alpha = -\frac{q}{p}$ Product of roots: $(a\alpha)(b\alpha) = ab\alpha^2 = \frac{r}{p}$ Now, consider the ratio: $\frac{ab\alpha^2}{(a+b)^2\alpha^2} = \frac{ab}{(a+b)^2}$ Substituting the values: $\frac{ab}{(a+b)^2} = \frac{r/p}{(-q/p)^2} = \frac{r}{p} 	imes \frac{p^2}{q^2} = \frac{pr}{q^2}$

If the ratio of the roots of the equation $px^2+qx+r=0$ is $a:b$, then $\frac{ab}{(a+b)^2}=$

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