If the roots of the quadratic equation $\sqrt{3}x^2 - kx + 2\sqrt{3...

Question

If the roots of the quadratic equation $\sqrt{3}x^2 - kx + 2\sqrt{3} = 0$ are real and equal, then the value(s) of $k$ is/are :

Accepted Answer

Step 1: For real and equal roots, discriminant $D = 0$.
Step 2: Here $a = \sqrt{3}$, $b = -k$, $c = 2\sqrt{3}$.
$$D = b^2 - 4ac = k^2 - 4(\sqrt{3})(2\sqrt{3}) = k^2 - 24$$
Step 3: $$k^2 - 24 = 0 \Rightarrow k^2 = 24 \Rightarrow k = \pm\sqrt{24}$$

Correct option : (A)

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