Question

Solve the following quadratic equation by the formula method : $3x^2+7x+2=0$.

Answer 1

Given equation is $3x^2+7x+2=0$
Comparing with $a{x}^2+bx+c=0$, we get
$a=3$, $b=7$, $c=2$
Then, $b^2-4ac={\left(7\right)}^2-4\times 3\times 2$
$=49-24=25$
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
$x=\frac{-7\pm \sqrt{25}}{2\times 3}$
$x=\frac{-7\pm 5}{6}$
$x=\frac{-7+5}{6}$ and $x=\frac{-7-5}{6}$
$x=\frac{-2}{6}$ and $x=\frac{-12}{6}$
Hence, $x=\frac{-1}{3}$ and $x=-2$ are the roots of the given quadratic equation.