Question

Solve each of the following equation, giving answer up to two decimal places.

$\left(ii\right)$ $3x^2-x-7=0$

Answer 1

Given equation: $3x^2-x-7=0$
Comparing $3x^2-x-7=0$ with $a{x}^2+bx+c=0$
We have $a=3,b=-1andc=-7$

We know that, for the equation $a{x}^2+bx+c=0$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ are roots of the equation.

$\Rightarrow x=\frac{-(-1)\pm \sqrt{(-1{)}^2-4\times 3\times (-7)}}{2\times 3}$

$\Rightarrow x=\frac{1\pm \sqrt{1+84}}{6}$

$\Rightarrow x=\frac{1\pm \sqrt{85}}{6}=\frac{1\pm 9.22}{6}$

$\Rightarrow x=\frac{10.22}{6}\text{or}x=\frac{-8.22}{6}$

$\therefore x=1.70\text{or}x=-\mathrm{1.37.}$