Question

What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = x2 − 4x + 5, and what does it mean about the number of real solutions the equation has?

The discriminant is −4, so the equation has 2 real solutions.
The discriminant is −4, so the equation has no real solutions.
The discriminant is 35, so the equation has 2 real solutions.
The discriminant is 35, so the equation has no real solutions.

Answer 1

a = 1, b = −4, c = 5, so discriminant = b^2 − 4ac = (−4)^2 − 4(1)(5) = 16 − 20 = −4.
Since the discriminant is negative, there are no real solutions (two complex conjugate roots).