Why Use This Tool?
Every quadratic equation ax² + bx + c = 0 is solved by the same formula — the discriminant b² − 4ac decides whether you get two roots, one double root, or none. This calculator applies the quadratic formula and explains the case.
The discriminant isn't just an intermediate value: positive means two distinct real roots, zero means both roots coincide, and negative means the parabola never touches the x-axis.
How It Works
- Enter coefficients a, b and c from your equation.
- Read the discriminant to understand the root situation.
- Get the roots — or the confirmation that no real roots exist.
Frequently Asked Questions
How do I solve a quadratic equation?
Apply the quadratic formula x = (−b ± √(b² − 4ac)) ÷ 2a. Enter your three coefficients and the calculator computes both roots with the discriminant shown.
What does the discriminant tell me?
Positive: two different real roots. Zero: one repeated root. Negative: no real roots — the solutions are complex numbers instead.
Why can't 'a' be zero?
Without the x² term the equation is linear, not quadratic — it has one root found by simple division, not the quadratic formula.
Tips & Things to Watch
- Check by substitution: plug a root back in and the equation should balance.
- A positive 'a' opens the parabola upward; negative opens downward.
- The vertex x-coordinate is −b/2a — halfway between the two roots.