Question

Solve each of the following equations for x and give, in each case, your answer correct to 2 decimal places:

(iv) $x^2-3x-9=0$

Answer 1

Compare $x^2-3x-9=0$ with $a{x}^2+bx+c=0$

$a=1,b=-3andc=-9$

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

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

$\Rightarrow x=\frac{-(-3)\pm \sqrt{(-3{)}^2-4(1\left)\right(-9)}}{2\left(1\right)}$

$\Rightarrow x=\frac{3\pm \sqrt{45}}{2}$

$\Rightarrow x=\frac{3\pm 6.70}{2}$

$\Rightarrow x=\frac{3+6.70}{2}andx=\frac{3-6.70}{2}$

$\therefore x=4.85and-1.85$.