Question

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

$\left(i\right)$ $x^2-5x-10=0$

Answer 1

Given equation: $x^2-5x-10=0$

Comparing $x^2-5x-10=0$ with $a{x}^2+bx+c=0$

We have $a=1,b=-5andc=-10$

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.

$\Rightarrow x=\frac{-(-5)\pm \sqrt{(-5{)}^2-4\times 1\times (-10)}}{2\times 1}$

$\Rightarrow x=\frac{5\pm \sqrt{25+40}}{2}$

$\Rightarrow x=\frac{5\pm \sqrt{65}}{2}=\frac{5\pm 8.06}{2}$

$\Rightarrow x=\frac{13.06}{2}\text{or}x=\frac{-3.06}{2}$

$\therefore x=6.53\text{or}x=-\mathrm{1.53.}$