If roots of the quadratic equation $x^2-k\sqrt{3}\,x+2=0$ are real ...

Question

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

Accepted Answer

Step 1: For real and equal roots, $D=b^2-4ac=0$.
Step 2: Here $a=1,\ b=-k\sqrt3,\ c=2$:
$$(-k\sqrt3)^2-4(1)(2)=0$$
Step 3: $3k^2-8=0\Rightarrow k^2=\dfrac{8}{3}$
Step 4: $k=\sqrt{\dfrac{8}{3}}$ (taking the value given in the options).
Answer: (B) $\sqrt{\dfrac{8}{3}}$

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