Question

Find the complete set of values of $a$ for which the quadratic equation $x^2-ax+(a+2)=0$ has equal roots.

Answer 1

The quadratic equation $x^2-ax+a+2=0$ has equal roots.

So, its discriminant is zero.

Thus, $D=b^2-4ac=0$

$a^2-4a-8=0$

Again applying the Quadratic formula for finding roots,

.So, $a=\frac{4\pm \sqrt{48}}{2}$ which gives $a=2+\sqrt{12},2-\sqrt{12}$ .