Question

What is the sum of all values of $m$ that satisfy $2m^2-16m+8=0$?

• A. $-8$
• B. $-4\sqrt{3}$
• C. $4\sqrt{3}$
• D. 8

Answer 1

The correct option is D 8

Consider the quadratic equation $2m^2-16m+8=0$ or $m^2-8m+4=0$

Find the roots of the equation $m^2-8m+4=0$ as shown below:

$m=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$=\frac{-(-8)\pm \sqrt{{(-8)}^2-4\left(1\right)\left(4\right)}}{2\left(1\right)}$

$=\frac{8\pm \sqrt{64-16}}{2}$

$=\frac{8\pm \sqrt{48}}{2}$

$=\frac{8\pm 2\sqrt{3}}{2}$

$=4\pm 2\sqrt{3}$

Hence, the sum of the values of $m$ is:

$4+2\sqrt{3}+4-2\sqrt{3}=8$