← Algebra II
Algebra II
The Discriminant
Lesson
The discriminant is the expression under the radical in the quadratic formula:
Without solving the equation, the sign of tells you how many real solutions a quadratic has.
- → two distinct real solutions.
- → one real solution (a double root).
- → no real solutions (the solutions are complex).
Worked example 1
.
Discriminant is 1 (positive) → two real solutions.
Worked example 2
.
Discriminant is −4 (negative) → no real solutions.
Practice
Work through these. Stuck? Click Get a hint.
Warm-Up
Quick problems to get going.
Problem 1
Problem 2
Problem 3
Problem 4
Practice
Standard problems matching the lesson.
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Challenge
Harder problems — edge cases, trickier numbers, multiple steps.
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22