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Question -

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



Answer -

Let’s consider theroots of the quadratic equation to be a and b.

Then, we have

We know that,

A quadratic equationcan be formed as,

x– x (Sum of roots) + (Product of roots) = 0

x2 – x (a + b) + (ab)= 0

x2 – 16x + 25 = 0 [Using (1) and (2)]

Therefore, therequired quadratic equation is x2 – 16x +25 = 0

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