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. $2+\sqrt{2}$
• B. $2\overline{+}\sqrt{1}2$
• C. $2-\sqrt{1}2$
• D. $-2-\sqrt{1}2$

Answer 1

The correct option is B

$2\overline{+}\sqrt{1}2$

Equal roots $\Rightarrow △=0$
$k^2-4(k+2)=0$
$k^2-4k-8=0$

$k=\frac{4\pm \sqrt{16+4\left(8\right)}}{2}$
$k=\frac{4\pm \sqrt{48}}{2}$
$k=\frac{4\pm 2\sqrt{12}}{2}$
$\therefore k=2\pm \sqrt{12}$