Use the discriminant to determine how many and what kind of solutions the quadratic equation x^(2)-x=1 has
The quadratic equation x^(2) - x = 1 can be rewritten in standard form as x^(2) - x - 1 = 0.
The discriminant of a quadratic equation is given by the formula: b^(2) - 4ac, where a = 1, b = -1, and c = -1 in this equation.
Therefore, the discriminant D = (-1)^(2) - 4(1)(-1) = 1 + 4 = 5.
Since the discriminant is positive, the quadratic equation has two real and distinct solutions.