Question

Solve the given quadratic equation by using the quadratic formula, $15m^2-11m+2=0$

Answer 1

The given quadratic equation $15m^2-11m+2=0$ is in the form $a{x}^2+bx+c=0$ where, $a=15,b=-11$ and $c=2$.

We know that according to the quadratic formula, the roots of quadratic equation are given by:

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

Substituting $a=15,b=-11$ and $c=2$ in above formula:

$x=\frac{-(-11)\pm \sqrt{(-11{)}^2-(4\times 15\times 2)}}{2\times 15}$

$=\frac{11\pm \sqrt{121-120}}{30}$

$=\frac{11\pm \sqrt{1}}{30}$

$=\frac{11\pm 1}{30}$

$x=\frac{11+1}{30}=\frac{12}{30}=\frac{6}{15}=\frac{2}{5}$

$x=\frac{11-1}{30}=\frac{10}{30}=\frac{1}{3}$

Hence, $x=\frac{2}{5}$ or $x=\frac{1}{3}$.