# Week 7 – Precalc 11

This week in Precalculus 11, we learned about interpreting the discriminant.

Real root: square root of a positive number

In the quadratic formula, the discriminant is $b^2$ – 4ac. By solving the discriminant, we can indicate how many real roots the equation has.

If $b^2$ – 4ac > 0, the equation has 2 real roots.

Example: 5$x^2$ – 9x + 4 = 0

$b^2$ – 4ac

= $(-9)^2$ – 4(5)(4)

= 81 – 20 · 4

= 81 – 80

= 1 -> 2 real roots

If $b^2$ – 4ac = 0, the equation has 1 real root.

Example: 2$x^2$ + 16x + 32 = 0

$b^2$ – 4ac

= $(16)^2$ – 4(2)(32)

= 256 – 8 · 32

= 256 – 256

= 0 -> 1 real root

If $b^2$ – 4ac < 0, the equation has 0 real roots.

Example: 6$x^2$ + 7 = 0

$b^2$ – 4ac

= $(0)^2$ – 4(6)(7)

= 0 – 24 · 7

= 0 – 168

= -168 -> 0 real roots

By interpreting the discriminant beforehand, we can determine whether or not to bother solving a quadratic equation.