What is the discriminant in algebra?

0/3

Examples

Lessons

Positive Discriminant
Without solving or graphing, determine the nature of the roots of the quadratic equation: $2x^2-12x+10=0$ $2 x^{2} - 12 x + 10 = 0$
Zero Discriminant
Without solving or graphing, determine the nature of the roots of the quadratic equation: $x^2+4=4x$ $x^{2} + 4 = 4 x$
Negative Discriminant
Without solving or graphing, determine the nature of the roots of the quadratic equation: $x^2+x+1=0$ $x^{2} + x + 1 = 0$

Topic Notes

The discriminant is actually part of the quadratic formula. It is super useful when we only need to determine whether a quadratic equation has 2 real solutions, 1 real solution, or 2 complex solutions.

• For the quadratic equation:

a{x^2} + bx + c = 0

quadratic formula:

x = \frac{{ - b \pm \sqrt {{b^2} - 4ac\;} \;}}{{2a}}

• discriminant: b² - 4ac
The discriminant (

\vartriangle

), b² - 4ac, can be used to discriminate between the different types of solutions:

b^2 - 4ac

> 0 : 2 solutions (2 real solutions)

b^2 - 4ac

= 0 : 1 solution (1 real solution)

b^2 - 4ac

< 0 : no solution (2 complex solutions)

Nature of roots of quadratic equations: The discriminant

Examples

Lessons

Free to Join!

Easily See Your Progress

Make Use of Our Learning Aids

Last Viewed

Practice Accuracy

Suggested Tasks

Earn Achievements as You Learn

Create and Customize Your Avatar

Topic Notes

Basic Concepts

Nature of roots of quadratic equations: The discriminant

Lessons

Easily See Your Progress

Make Use of Our Learning Aids

Last Viewed

Practice Accuracy

Suggested Tasks

Earn Achievements as You Learn

Create and Customize Your Avatar

Become a member to get more!