When b^(2) - 4ac > 0 How many solutions does it have? (Quadratic formula)?

The discriminant is that part of the quadratic equation under the square root symbol.

Specifically:

d = b² - 4ac

The sign of the discriminant tells you how many real roots there are.

d > 0 (positive) --> 2 real roots

d = 0 (zero) --> 1 real (double) root

d < 0 (negative) --> 0 real roots (and 2 complex roots)

Answer:

2 real roots

f(x) = ax^2 + bx + c has two real roots if b^2 - 4ac > 0.