Question

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

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

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

Answer 1

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

In $a{x}^2+bx+c=0$

Discriminant $D=b^2-4ac$

If $D=0$, so they have equal and real roots.

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

$a=2$, $b=k$ and $c=3$

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

$\Rightarrow k^2-24=0$

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

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