Question

$x^2+5x-(a^2+a-6)=0$.

Answer 1

formula for roots of quadratic

expression $a{x}^2+bx+c=0$ is

$=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

So for $x^2+5x-(a^2+a-6)=$

$\Rightarrow \frac{-5\pm \sqrt{25+4(a^2+a-6)}}{2}$

$\Rightarrow \frac{-5\pm \sqrt{4a^2+4a+1}}{2}$

$\Rightarrow \frac{-5}{2}\pm \sqrt{(a+1/2{)}^2}$

$=\frac{-5}{2}\pm (a+1/2)$