Question

Solve the quadratic equation $6x^2-x-12=0$ by using the quadratic formula.

Answer 1

Determining the value of $x$ by using the quadratic formula

The quadratic formula is $\begin{array}{rcl}x& =& \frac{-b\pm \sqrt{b^2-4ac}}{2a}\end{array}$.

For the given equation $6x^2-x-12=0$, the value of variables are $a=6,b=-1$ and $c=-12$.

Substituting the values of $a,b$ and $c$ in quadratic formula,

$$\begin{gathered} x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \Rightarrow x=\frac{-(-1)\pm \sqrt{{(-1)}^2-4\left(6\right)(-12)}}{2\left(6\right)} \\ \Rightarrow x=\frac{1\pm \sqrt{1+288}}{12} \\ \Rightarrow x=\frac{1\pm \sqrt{289}}{12} \\ \Rightarrow x=\frac{1\pm 17}{12} \\ \Rightarrow x=\frac{1-17}{12},\frac{1+17}{12} \\ \Rightarrow x=-\frac{16}{12},\frac{18}{12} \end{gathered}$$

$\therefore x=-\frac{4}{3},\frac{3}{2}$

Therefore, the roots of the equation are $-\frac{4}{3}$, $\frac{3}{2}$.