Question

In the given, determine whether the given quadratic equation has real roots and if so, find the roots.
$9x^2+7x-2=0$

Answer 1

The given equation is $9x^2+7x-2=0$

Here $a=9,b=7,c=2$

$\therefore D=b^2-4ac={\left(7\right)}^2-4\times 9\times -2=121>0$

So, the given equation has real roots given by

$\alpha =\frac{-b+\sqrt{D}}{2a}=\frac{-7+\sqrt{121}}{2\times 9}=\frac{2}{9}$
$\beta =\frac{-b-\sqrt{D}}{2a}=\frac{-7-\sqrt{121}}{2\times 9}=-1$