If AM and GM of roots of a quadratic equation are 8 and 5 respectively, then obtain the quadratic equation.

Question

Philoid · Accepted Answer

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

According to the given condition,

⇒

⇒ a + b = 16 …..(1)

⇒ GM = √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 x² – 16x + 25 = 0.