The quadratic equation in t,such that the Ari | vedclass

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Question

(A) Let the roots of the quadratic equation be $\alpha$ and $\beta$.The Arithmetic Mean $(A.M.)$ of the roots is given by $A = \frac{\alpha + \beta}{2

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$t^2 - 2At + G^2 = 0$

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(A) Let the roots of the quadratic equation be $\alpha$ and $\beta$.The Arithmetic Mean $(A.M.)$ of the roots is given by $A = \frac{\alpha + \beta}{2}$,which implies $\alpha + \beta = 2A$.The Geometric Mean $(G.M.)$ of the roots is given by $G = \sqrt{\alpha \beta}$,which implies $\alpha \beta = G^2$.$A$ quadratic equation with roots $\alpha$ and $\beta$ is given by the formula $t^2 - (	ext{sum of roots})t + (	ext{product of roots}) = 0$.Substituting the values,we get $t^2 - (2A)t + G^2 = 0$,or $t^2 - 2At + G^2 = 0$.

The quadratic equation in $t$,such that the Arithmetic Mean $(A.M.)$ of its roots is $A$ and the Geometric Mean $(G.M.)$ is $G$,is

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