Question

For what values of k will the quadratic equation : ${3x}^2+kx+3=0$ have real equal roots?

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

Answer 1

The correct option is C $\pm 6$

${3x}^2+kx+3=0$
Here, $a=3,b=k,c=3$
Now, $D=b^2-4ac=k^2-4\times 3\times 3k^2-36$
We know that a quadratic equation has real and equal roots,
If $D=0\Rightarrow k^2-36=0\Rightarrow k^2=36$
$\therefore k=\pm \sqrt{36}=\pm 6$