Answer
$\displaystyle \frac{4-\sqrt{6}}{2}$ and $\displaystyle \frac{4+\sqrt{6}}{2}$
are to be excluded from the domain
Work Step by Step
Excluded from the domain are all values of x that yield 0 in the denominator.
These values are solutions of
$2x^{2}-8x+5=0 \; $... apply the quadratic formula
$x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}=\frac{8\pm\sqrt{(-8)^{2}-4(2)(5)}}{2(2)}$
$=\displaystyle \frac{8\pm\sqrt{24}}{4}=\frac{8\pm 2\sqrt{6}}{4}$
$=\displaystyle \frac{2(4\pm\sqrt{6})}{4}=\frac{4\pm\sqrt{6}}{2}$
$\displaystyle \frac{4-\sqrt{6}}{2}$ and $\displaystyle \frac{4+\sqrt{6}}{2}$
are to be excluded from the domain.
