If the Arithmetic Mean (A.M.) and Geometric M | vedclass

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(D) Let the roots of the quadratic equation be $\alpha$ and $\beta$.Given that the Arithmetic Mean ($A$.$M$.) of the roots is $p$,we have $\frac{\alph

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$x^{2}-2px+q^{2}=0$

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(D) Let the roots of the quadratic equation be $\alpha$ and $\beta$.Given that the Arithmetic Mean ($A$.$M$.) of the roots is $p$,we have $\frac{\alpha+\beta}{2} = p$,which implies $\alpha+\beta = 2p$.Given that the Geometric Mean ($G$.$M$.) of the roots is $q$,we have $\sqrt{\alpha\beta} = q$,which implies $\alpha\beta = q^{2}$.$A$ quadratic equation with roots $\alpha$ and $\beta$ is given by $x^{2} - (	ext{sum of roots})x + (	ext{product of roots}) = 0$.Substituting the values,we get $x^{2} - (2p)x + q^{2} = 0$,which simplifies to $x^{2} - 2px + q^{2} = 0$.

If the Arithmetic Mean ($A$.$M$.) and Geometric Mean ($G$.$M$.) of the roots of a quadratic equation in $x$ are $p$ and $q$ respectively,then the equation is:

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