with real
coefficients a, b, and c, when a ¹ 0, areSECTION 6.2 THE QUADRATIC FORMULA AND THE DISCRIMINANT
Quadratic Formula:
The solutions of the quadratic equation with real
coefficients a, b, and c, when a ¹ 0, are
The 
is called the discriminant.
If the discriminant > 0, there will be 2 distinct real solutions to the equation .
If the discriminant = 0, there will be 1 distinct real solution (double root) to the
equation .
If the discriminant < 0, there will be no real solutions.
EXAMPLES:
1.
2.
3.
Since we cannot take the square root of -8 in the real number system, there is no real solution to this equation.