(D) Let $a$ and $b$ be the roots of the quadratic equation.Then,the quadratic equation is given by $x^2-(a+b)x+ab=0$ ....$(i)$It is given that $AM = 5

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(D) Let $a$ and $b$ be the roots of the quadratic equation.Then,the quadratic equation is given by $x^2-(a+b)x+ab=0$ ....$(i)$It is given that $AM = 5$ and $GM = 4$.Therefore,$\frac{a+b}{2} = 5 \Rightarrow a+b = 10$.And $\sqrt{ab} = 4 \Rightarrow ab = 16$.Substituting these values into equation $(i)$,we get $x^2-10x+16=0$.Thus,the required quadratic equation is $x^2-10x+16=0$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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If $AM$ and $GM$ of roots of a quadratic equation are $5$ and $4$,respectively,then the quadratic equation is

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$x^2-10x-16=0$
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$x^2+10x+16=0$
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$x^2+10x-16=0$
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$x^2-10x+16=0$

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