Question

The roots of the given equation $x+5=\frac{2x+10}{x-6}$ are

• A. $8,-5$
• B. $-8,-5$
• C. $-8,5$

Answer 1

The correct option is A $8,-5$

Given, $x+5=\frac{2x+10}{x-6}$

$\Rightarrow (x+5)(x-6)=(2x+10)\Rightarrow x^2-3x-40=0$

For the standard form of a quadratic equation ax² + bx + c = 0, roots are $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.

Here, $a=1,b=-3$ and $c=-40$.

$\therefore$ Roots of the quadratic equation are:
$x=\frac{-(-3)\pm \sqrt{3^2-4\times 1\times (-40)}}{2\times 1}=\frac{3\pm \sqrt{9+160}}{2}=\frac{3\pm \sqrt{169}}{2}=\frac{3\pm 13}{2}\Rightarrow x=\frac{3+13}{2}\text{or}\frac{3-13}{2}=\frac{16}{2}\text{or}\frac{-10}{2}=8\text{or}-5$

Hence, roots of the equation
$x+5=\frac{2x+10}{x-6}$ are $8,-5.$