Use the discriminant to determine how many and what kind of solutions the quadratic equation x^2-x=1 has.
The quadratic equation given is x^2 - x = 1. This equation can be rewritten as x^2 - x - 1 = 0.
The discriminant of a quadratic equation in the form ax^2 + bx + c = 0 is given by the formula discriminant = b^2 - 4ac.
In this case, a=1, b=-1, and c=-1. So, the discriminant for the equation x^2 - x - 1 = 0 is:
b^2 - 4ac = (-1)^2 - 4(1)(-1) = 1 + 4 = 5
Since the discriminant is positive (5 > 0), the quadratic equation x^2 - x - 1 = 0 has two distinct real roots.