Question

The complete set of values of $k$, for which the quadratic equation $x^2-kx+k+2=0$ has equal roots, consists of:

• A. $2+\sqrt{12}$
• B. $2\pm \sqrt{12}$
• C. $2-\sqrt{12}$
• D. $-2-\sqrt{12}$

Answer 1

The correct option is B $2\pm \sqrt{12}$

Since, $x^2-kx+k+2=0$ has equal roots.

So, Discriminant = $D=0⟹k^2-4(k+2)=0⟹k^2-4k-8=0⟹k=2\pm \sqrt{12}$ ( $D=b^2-4ac$ )