1. The Discriminant
How to Use the Discriminant to
Describe the Types of Solutions of
a Quadratic Equation

2. • Standard form of a quadratic equation, where a,
b, and c are integers
• Quadratic Formula:

3. The Discriminant
• The part under the square root in the Quadratic
Formula:
• Make sure your quadratic equation is in
standard form (= 0) before substituting in for a,
b, and c

4. Types of Roots
Value of Discriminant Types of Roots (or Answers)
Positive and a Perfect Square (like 25 2 real, rational roots (integers or
or 49) fractions for answers, no square roots)
Positive and Not a Perfect Square (like 2 real, irrational roots (will have a
119 or 2) square root left in the answer)
0 1 real, rational root (integer or fraction
for answer, no square root)
Negative (like -47 or -20) 2 imaginary (or complex) roots
(answers have i )

5. Examples
Find the value of the 1. First, put it in standard form:
discriminant and
use it to describe 2. Plug into the discriminant:
the roots of the
equation:
3. Get the answer: -76
4. Use the chart to describe the
solutions:
2 imaginary answers