Question

Find the roots of the equation $x+5=\frac{2x+10}{x-6}$ using the quadratic formula.

• A. $8,5$
• B. $-3,5$
• C. $1,2$
• D. $8,-5$

Answer 1

The correct option is D $8,-5$

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

$\Rightarrow (x+5)(x-6)=(2x+10)\Rightarrow x^2-x-30=2x+10\Rightarrow x^2-3x-40=0$

For the standard form of 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:

$x=\frac{-(-3)\pm \sqrt{(-3{)}^2-(4\times 1\times 40)}}{2\times 1}=\frac{3\pm \sqrt{9+160}}{2}=\frac{3\pm \sqrt{169}}{2}=\frac{3\pm 13}{2}\Rightarrow x=\frac{3+13}{2},x=\frac{3-13}{2}\Rightarrow x=\frac{16}{2},x=\frac{-10}{2}\Rightarrow x=8,x=-5$

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