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

Asked by Abhisek | 1 year ago |  91

##### Solution :-

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

Then, we have

A.M. = $$\dfrac{a+b}{2}=8$$

a+b = 16 ............(1)

G.M. = $$\sqrt{ab}$$ = 5

ab = 25 ...........(2)

We know that,

A quadratic equation can 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, the required quadratic equation is x2 – 16x + 25 = 0

Answered by Abhisek | 1 year ago

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