# How do you find the discriminant of x^2-2x+1=0 and use it to determine if the equation has one, two real or two imaginary roots?

Apr 10, 2017

The discriminant of an equation of the form, $y = a {x}^{2} + b x + c$, is:

$d = {b}^{2} - 4 \left(a\right) \left(c\right)$ If $d \left\{\begin{matrix}= 0 \text{ & one real root" \\ > 0" & two real roots" \\ <0" & two imaginary roots}\end{matrix}\right.$

#### Explanation:

Given: ${x}^{2} - 2 x + 1 = 0$

$a = 1 , b = - 2 , \mathmr{and} c = 1$

$d = {b}^{2} - 4 \left(a\right) \left(c\right)$

$d = {\left(- 2\right)}^{2} - 4 \left(1\right) \left(1\right)$

$d = 0$, then one real root