The Discriminant: D = b² - 4 a c D = (-2)² - 4 · 1 · 5 = 4 - 20 = - 16 D = - 16 D < 0 , which means that there are no real solutions. The solutions of this equation are complex conjugate numbers.
For a quadratic equation ax^2 + bx + c = 0, the discriminant is given by b^2 - 4ac Thus for a^2 - 2a + 5 = 0, a = 1, b = -2 and c = 5 b^2 - 4ac = (-2)^2 - 4(1)(5) = 4 - 20 = -16
