# How do you find the roots, real and imaginary, of y=x^2 - 5/2x + 1/2  using the quadratic formula?

May 3, 2017

$x = \frac{5 \pm \sqrt{17}}{4}$

#### Explanation:

If an equation is $a {x}^{2} + b x + c = 0$
Then $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
To solve this equation
You can judge by this pattern ${b}^{2} - 4 a c$
So $\frac{25}{4} - 4 \cdot 1 \cdot \frac{1}{2} > 0$
This result imply us exist 2 real roots you can find
Thus begin solving
$x = \frac{\left(\frac{5}{2}\right) \pm \sqrt{\frac{25}{4} - 4 \cdot 2 \cdot \frac{1}{2}}}{2}$
$x = \frac{5 \pm \sqrt{17}}{4}$