If the A.M. and G.M. of the roots of a quadra | vedclass

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(C) Let the roots of the quadratic equation be $\alpha$ and $\beta$.The standard form of a quadratic equation is $x^2 - (	ext{sum of roots})x + (	ex

Vedclass · Accepted Answer

$x^2 - 16x + 25 = 0$

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(C) Let the roots of the quadratic equation be $\alpha$ and $\beta$.The standard form of a quadratic equation is $x^2 - (	ext{sum of roots})x + (	ext{product of roots}) = 0$.Given the Arithmetic Mean $(A.M.)$ of the roots is $8$:$\frac{\alpha + \beta}{2} = 8 \Rightarrow \alpha + \beta = 16$.Given the Geometric Mean $(G.M.)$ of the roots is $5$:$\sqrt{\alpha \beta} = 5 \Rightarrow \alpha \beta = 25$.Substituting the sum and product of the roots into the standard form:$x^2 - (16)x + (25) = 0$.Thus,the required quadratic equation is $x^2 - 16x + 25 = 0$.

If the $A.M.$ and $G.M.$ of the roots of a quadratic equation are $8$ and $5$ respectively,then the quadratic equation will be

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