If the arithmetic mean of the roots of a quadratic equation is and the geometric mean is , then the equation is
Explanation for the correct option.
Step 1: Find the sum and product of roots.
Given that, the arithmetic mean of the roots of a quadratic equation is and the geometric mean is .
Let the roots of the quadratic equation be .
By definition of arithmetic & geometric mean we have:
And
Step 2: Find the quadratic equation.
We know that the quadratic equation is of the form:
On substituting the value of sum and product of root from step in general form of quadratic equation, we get;
Hence, option C is correct.