Question

Solve each of the following equations for x, giving your answer correct to 3 decimal places:

(i) $3x^2-12x-1=0$

Answer 1

Compare $3x^2-12x-1=0$ with $a{x}^2+bx+c=0$

$a=3,b=-12andc=-1$

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

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

$\Rightarrow x=\frac{-(-12)\pm \sqrt{(-12{)}^2-4(3\left)\right(-1)}}{2\left(3\right)}$

$\Rightarrow x=\frac{12\pm \sqrt{144+12}}{6}$

$\Rightarrow x=\frac{12\pm \sqrt{156}}{6}$

$\Rightarrow x=\frac{12\pm 12.489}{6}$

$\Rightarrow x=\frac{12+12.489}{6}andx=\frac{12-12.489}{6}$

$\therefore x=4.082and-0.082$.