#### Question

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

#### Solution

Let the root of the quadratic equation be *a* and *b*.

According to the given condition,

The quadratic equation is given by,

*x*^{2}– *x* (Sum of roots) + (Product of roots) = 0

*x*^{2} – *x* (*a* + *b*) + (*ab*) = 0

*x*^{2} – 16*x* + 25 = 0 [Using (1) and (2)]

Thus, the required quadratic equation is *x*^{2} – 16*x* + 25 = 0

Is there an error in this question or solution?

Solution If A.M. and G.M. of Roots of a Quadratic Equation Are 8 and 5, Respectively, Then Obtain the Quadratic Equation. Concept: Relationship Between A.M. and G.M..