Discriminant Formula

beginneralgebraquadratic equations

Determines the nature of roots in a quadratic equation

The Formula

Δ = b² - 4ac

Variables & Symbols

Δ

Discriminant

a

Coefficient of x²

b

Coefficient of x

c

Constant term

When to Use This Formula

  • To determine if roots are real or complex
  • To check if roots are equal or distinct
  • Before applying the quadratic formula
  • In optimization problems

Worked Examples

Example 1

Problem:

Find the discriminant of x² + 5x + 6 = 0

Solution: Δ = 1 (two distinct real roots)

Step-by-Step:

1

Identify: a=1, b=5, c=6

2

Apply formula: Δ = 5² - 4(1)(6)

3

Δ = 25 - 24 = 1

4

Since Δ > 0, two distinct real roots exist

Common Mistakes to Avoid

  • Forgetting to multiply by 4
  • Sign errors with negative coefficients
  • Misinterpreting the discriminant value

Real-World Applications

1

Checking if a system has real solutions

2

Analyzing market equilibrium points in economics

3

Determining if collision will occur in physics

Practice Problems

Problem 1: Find Δ for x² - 4x + 4 = 0

Show Answer

Answer: Δ = 0

Problem 2: Find Δ for x² + 2x + 5 = 0

Show Answer

Answer: Δ = -16

Related Formulas

quadratic formula

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nature of roots

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Tags:

algebraquadraticdiscriminantroots

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