Quadratic Equations

1. Understand the problem:

We are given the Arithmetic Mean (A.M.) and Geometric Mean (G.M.) of the roots of a quadratic equation as 5 and 4, respectively. We need to find the quadratic equation from the given options.

2. Let the roots be and :

The A.M. of the roots is given by:

The G.M. of the roots is given by:

3. Form the quadratic equation:

A quadratic equation with roots and is:

Substituting the values:

Correct Answer: (D)