The Discriminant

The discriminant is part of the quadratic formula, and it tells us how many answers there may be.

    \[\mathbf{b^2-4ac}\]

Example 1: x^2-8x+18=0

a=1

b=-8

c=18

Plug into the discriminant formula to get.

    \[(-8)^2-4(1)(18)\]

    \[= 64-72\]

 

    \[=-8\]

 

Example 2: 2x^2+3x-10

a=2

b=3

c=-10

    \[3^2-4(2)(-10)\]

    \[= 9+80\]

    \[=89\]

 

Types of Discriminants

There are three main types of discriminants: positive , negative, and 0.

  1. A positive discriminant says that there are 2 solutions to the quadratic equation. Examples (2) and (3) are positive, so that means they have possible solutions.
  2. A negative discriminant means that there is NO SOLUTION to the quadratic equation. Example (1) had a negative discriminant, so there was no solution.
  3. A discriminant of 0 means that there is only 1 solution to the quadratic equation.