Question

The quadratic equation in x such that the arithmetic mean of the roots is p and the geometric mean is q is

• A.
• B.
• C.
• D. none of these

Answer 1

The correct option is D

none of these

A quadratic equation can be written as

$x^2$ - (sum of roots)x + (product of roots) =0

Arithmetic mean(p) = $\frac{\text{Sum of roots}}{2}\Rightarrow$ sum of roots = 2p

Geometric mean (q) = $\sqrt{\text{(Product of roots)}}\Rightarrow$ product of roots = $q^2$

The required equation is $x^2-2px+q^2=0$