(A) Let the roots of the quadratic equation be $\alpha$ and $\beta$.The arithmetic mean $(AM)$ is given by $\frac{\alpha + \beta}{2} = 9$,which implie

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(A) Let the roots of the quadratic equation be $\alpha$ and $\beta$.The arithmetic mean $(AM)$ is given by $\frac{\alpha + \beta}{2} = 9$,which implies $\alpha + \beta = 18$.The geometric mean $(GM)$ is given by $\sqrt{\alpha \beta} = 4$,which implies $\alpha \beta = 16$.$A$ quadratic equation with roots $\alpha$ and $\beta$ is given by the formula $x^2 - (\alpha + \beta)x + \alpha \beta = 0$.Substituting the values of $(\alpha + \beta)$ and $\alpha \beta$,we get $x^2 - 18x + 16 = 0$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Relation between roots and coefficients

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If the arithmetic mean and geometric mean of the two roots of a quadratic equation are $9$ and $4$ respectively,then what is the quadratic equation?

A
$x^2 - 18x + 16 = 0$
B
$x^2 + 18x - 16 = 0$
C
$x^2 + 18x + 16 = 0$
D
$x^2 - 18x - 16 = 0$

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4-2.Quadratic Equations and Inequations

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Relation between roots and coefficients

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If the arithmetic mean and geometric mean of the two roots of a quadratic equation are $9$ and $4$ respectively,then what is the quadratic equation?

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