What is the sum of the two values which will make the following expression undefined? $$\frac{x-3}{2x^2-8x+7}$$
I notice that the expression will be undefined when the denominator is zero, since I cannot divide by zero. In this case, $a=2, b=-8, c=7$, so plugging these values into the formula, I get $$x=\frac{-(-8)\pm\sqrt{(-8)^2-4(2)(7)}}{2(2)}$$ Simplifying the expression, I get $$x=\frac{8\pm\sqrt{64-56}}{4}=\frac{8\pm\sqrt{8}}{4}=\frac{8\pm 2\sqrt{2}}{4}=\frac{4\pm\sqrt{2}}{2}$$ To find their sum, I just add them together: $$\frac{4+\sqrt{2}}{2}+\frac{4-\sqrt{2}}{2}=\frac{4+\sqrt{2}+4-\sqrt{2}}{2}=\frac{8}{2}=4$$ 