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If $A . M$ and $G . M$ of roots of a Quadratic Equation are $8$ and $5$ then Quadratic Equation is

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x^{2} + 16 x - 25 = 0

None of these

x^{2} - 16 x + 25 = 0

x^{2} + 10 x + 25 = 0

answer is B.

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Detailed Solution

A . M = \frac{a + b}{2} = 8 \Rightarrow a + b = 16 \to (1)

$G . M = \sqrt{a b} = 5 \Rightarrow a b = 25 \to (2)$

The Quadratic Equation is

$x^{2} - x (sum of roots) + (product of roots) = 0$

$x^{2} - x (a + b) + a b = 0$

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

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