Question

In the given, determine whether the given quadratic equation has real roots and if so, find the roots.
$x^2+5x+5=0$

Answer 1

The given equation is $x^2+5x+5=0$

Here, $a=1,b=5,c=5$

$\therefore D=b^2-4ac={\left(25\right)}^{}-4\times 1\times 5=5>0$

So, the given equation has real roots given by

$\alpha =\frac{-b+\sqrt{D}}{2a}=\frac{-1+\sqrt{49}}{2\times 6}=\frac{1}{2}$

$\beta =\frac{-b-\sqrt{D}}{2a}=\frac{-1-\sqrt{49}}{2\times 6}=\frac{-2}{3}$