Question

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

Answer 1

Let the root of the quadratic equation be a and b.
According to the given condition,
$A.M. = \frac{a + b }{ 2} = 8 ⇒ a + b = 16 ...(1)$
$G.M. = \sqrt{ab} = 5 ⇒ab = 25 ...(2)$
The quadratic equation is given by,
x2- x (Sum of roots) + (Product of roots) = 0
x2- x (a + b) + (ab) = 0
x2-16x + 25 = 0 [Using (1) and (2)]
Thus, the required quadratic equation is x 2 -16x + 25 = 0.