What does the discriminant tell you?

If b² − 4ac > 0 there are two real roots; if it equals 0 there is one; if it is negative there are no real roots.

When should you use the quadratic formula instead of factoring?

When the quadratic does not factor with simple integers — the formula always works.

Grade 11 · Mathematics

Quadratic formula

Why it matters

The general solution.

Core20m readingPrerequisite: Factoring

What is the quadratic formula?

Short answer

The quadratic formula solves any quadratic equation ax² + bx + c = 0 for x: x = (−b ± √(b² − 4ac)) / (2a). It works even when the quadratic cannot be factored easily. The expression under the root, b² − 4ac, is the discriminant, which tells you how many real solutions the equation has.

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Frequently asked questions

What does the discriminant tell you?: If b² − 4ac > 0 there are two real roots; if it equals 0 there is one; if it is negative there are no real roots.
When should you use the quadratic formula instead of factoring?: When the quadratic does not factor with simple integers — the formula always works.

What is the quadratic formula?

Related topics

Frequently asked questions