Question

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?

Answer 1

The discriminant of an equation of the form, `y = ax^2+bx+c`, is:

`d = b^2-4(a)(c)` If `d{(=0", one real root"),( > 0", two real roots"),(<0", two imaginary roots"):}`

Explanation:

Given: `x^2-2x+1=0`

`a = 1, b = -2, and c = 1`

`d = b^2-4(a)(c)`

`d = (-2)^2-4(1)(1)`

`d = 0`, then one real root