This week in pre-calculus 11, we learned about the discriminant. The discriminant is the radicand in the quadratic formula, b²– 4ac.

The discriminant is used to indicate whether the quadratic formula has 2 real roots or unequal roots, 1 real root or 2 equal roots, or no real roots.

x > 0: 2 real roots / 2 unequal roots.

x = 0: 1 real root / 2 equal roots.

x < 0: 0 real roots.

We use the quadratic equation to figure out which numbers are a, b, and c.

ax² + bx + c = 0

Ex:

4x² + 3x + 8 = 0

a = 4, b = 3, c = 8

b²– 4ac

3²– 4(4)(8)

9 – 128

= -119

Seeing as the answer is negative, there are no real roots because -119 is less than 0.