Question

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

(ii) $4x+\frac{6}{x}+13=0$

Answer 1

Given: $4x+\frac{6}{x}+13=0$

$\Rightarrow \frac{4x^2+6+13x}{x}=0$

$\Rightarrow 4x^2+13x+6=0$

Compare $4x^2+13x+6=0$ with the equation $a{x}^2+bx+c=0$

$a=4,b=13andc=6$

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

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

$\Rightarrow x=\frac{-13\pm \sqrt{(13{)}^2-4(4\left)\right(6)}}{2\times 4}$

$\Rightarrow x=\frac{-13\pm \sqrt{169-96}}{8}$

$\Rightarrow x=\frac{-13\pm \sqrt{73}}{8}$

$\Rightarrow x=\frac{-13\pm 8.54}{8}$

$\Rightarrow x=\frac{-13+8.54}{8}andx=\frac{-13-8.54}{8}$

$\therefore x=-0.56and-2.69$.