The Discriminant
The Quadratic Discriminant
The discriminant is the expression b² − 4ac inside the quadratic formula. Its value tells you how many real roots a quadratic equation has.
What is the discriminant?
For a quadratic written as ax² + bx + c = 0, the discriminant is Δ = b² − 4ac. The coefficients a, b, and c include their signs.
Identify a, b, and c
- Write the equation in standard form ax² + bx + c = 0.
- Read a from the x² term.
- Read b from the x term, including its sign.
- Read c from the constant term.
- Substitute them into b² − 4ac.
Worked example
Identify the coefficients in 2x² − 7x + 3
- a = 2
- b = −7
- c = 3
Δ = (−7)² − 4(2)(3) = 49 − 24 = 25.
Common mistakes
- Dropping the negative sign from b.
- Assuming a missing x term has b = 1 instead of b = 0.
- Forgetting that an unwritten coefficient of x² is 1.
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