Question

The value of $a$ for which the equation $2x^2+2\sqrt{6}x+a=0$ has equal roots is:

• A. $3$
• B. $4$
• C. $2$
• D. $\sqrt{3}$
• E. $\sqrt{2}$

Answer 1

The correct option is A

$3$

Explanation for the correct option:

Find the value of $a$:

An equation $2x^2+2\sqrt{6}x+a=0$ given.

Since, it is given that the given quadratic equation has equal roots.

We know that, if a quadratic equation has equal roots then the discriminant is zero.

Discriminant of a quadratic equation is given by, $D=b^2-4ac$

So, ${\left(2\sqrt{6}\right)}^2-4\left(2\right)\left(a\right)=0$

$$\begin{gathered} 24-8a=0 \\ \Rightarrow 8a=24 \\ \Rightarrow a=3 \end{gathered}$$

Therefore, The value of $a$ for which the equation $2x^2+2\sqrt{6}x+a=0$ has equal roots is $3$.

Hence, option (A), $3$ is the correct answer.