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. $-2-\sqrt{2}$

Answer 1

The correct option is B

$2\pm \sqrt{12}$

$\text{Since the equation has real roots.}\Rightarrow D=0\Rightarrow b^2-4ac=0\Rightarrow k^{2}4\left(1\right)(k+2)=0\Rightarrow k^2-4k-8=0\Rightarrow k=\frac{4\pm \sqrt{16-4\left(1\right)(-8)}}{2\left(1\right)}\Rightarrow k=\frac{4\pm 2\sqrt{12}}{2}\Rightarrow k=2\pm \sqrt{12}$