Question

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

(iii) $2x^2+11x+4=0$

Answer 1

Compare $2x^2+11x+4=0$ with $a{x}^2+bx+c=0$

$a=2,b=11andc=4$

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

$\Rightarrow x=\frac{-11\pm \sqrt{(11{)}^2-4(2\left)\right(4)}}{2\left(2\right)}$

$\Rightarrow x=\frac{-11\pm \sqrt{89}}{4}$

$\Rightarrow x=\frac{-11\pm 9.433}{4}$

$\Rightarrow x=\frac{-11+9.433}{4}$ and $x=\frac{-11-9.433}{4}$

$\therefore x=-0.392$ and $-\mathrm{5.108.}$