Answer
$\displaystyle \frac{5}{2}$ and 1
Work Step by Step
$2r^{2}-7r+5=0$
Use the quadratic formula:
(For $ax^{2}+bx+c=0,\ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ )
$r=\displaystyle \frac{-(-7)\pm\sqrt{(-7)^{2}-4(2)(5)}}{2(2)}$
$=\displaystyle \frac{7\pm\sqrt{49-40}}{4}=\frac{7\pm\sqrt{9}}{4}$
$r=\displaystyle \frac{7\pm 3}{4}$
$r=\displaystyle \frac{7+3}{4}$ or $r=\displaystyle \frac{7-3}{4}$
$r=\displaystyle \frac{10}{4}$ or $r=\displaystyle \frac{4}{4}$
$r=\displaystyle \frac{5}{2}$ or $r=1$
Solutions:
$\displaystyle \frac{5}{2}$ and 1.
