Question

The G.M of the roots of the equation $x^2-18x+9=0$ is

• A. $3$
• B. $4$
• C. $2$
• D. $1$

Answer 1

The correct option is A

$3$

Explanation for the correct option:

Find the geometric mean of the roots of the given equation.

A quadratic equation $x^2-18x+9=0$ is given.

Assume that, $\alpha$ and $\beta$ be the roots of the given equation.

So, the geometric mean $G.M$ is given by:

$G.M=\sqrt{\alpha \beta }$

We know that the product of roots is given by $\frac{c}{a}=9$.

Therefore,

$$\begin{gathered} G.M=\sqrt{9} \\ \Rightarrow G.M=3 \end{gathered}$$

So, the geometric mean of the roots of the given quadratic equation is $3$.

Hence, option $A$ is the correct answer.