Question

Find the values of $k$ for each of the following quadratic equation, so that they have two real equal roots.

$2x^2+kx+3=0$

• A. $k=\pm 2\sqrt{3}$
• B. $k=\pm \sqrt{3}$
• C. $k=\pm 2\sqrt{6}$
• D. $k=\pm \sqrt{6}$

Answer 1

The correct option is C $k=\pm 2\sqrt{6}$

Given, $2x^2+kx+3=0$

Comparing with the standard quadratic equation is $a{x}^2+bx+c=0$

We get, $a=2,b=k,c=3$

Given that the quadratic equation has two real equal roots.

Thus, the discriminant is $=0$

Here, $D=b^2-4ac=0$

$\Rightarrow k^2-4\times 2\times 3=0$

$\Rightarrow k^2-24=0$

$\Rightarrow k^2=24$

$\Rightarrow k=\pm \sqrt{24}$

$\Rightarrow k=\pm \sqrt{2\times 2\times 2\times 3}$

$\Rightarrow k=\pm 2\sqrt{6}$