Quadratic Equation Solver
Solve ax² + bx + c = 0. Finds discriminant and roots.
What is a quadratic equation and how does this solver work?
A quadratic equation is a second‑degree polynomial of the form ax² + bx + c = 0, where a ≠ 0. This solver uses the quadratic formula: x = (–b ± √Δ) / 2a, where the discriminant Δ = b² – 4ac determines the nature of the roots. If Δ > 0, there are two distinct real roots. If Δ = 0, there is one double root. If Δ < 0, the equation has two complex conjugate roots. The calculator displays all three values: the discriminant and both roots.
How to use the Quadratic Equation Solver
Enter the coefficients a, b, and c of your quadratic equation. Coefficient a must not be zero (otherwise it's not a quadratic equation). Click "Calculate" to instantly see the discriminant, the nature of the roots, and the exact numerical values. The solver handles negative, decimal, and fractional coefficients.
Example calculations
x² – 3x + 2 = 0 (a=1, b=–3, c=2): Δ = 9 – 8 = 1, roots: x₁ = 2, x₂ = 1. x² – 2x + 5 = 0 (a=1, b=–2, c=5): Δ = 4 – 20 = –16, two complex roots: 1 + 2i and 1 – 2i. x² – 6x + 9 = 0 (a=1, b=–6, c=9): Δ = 0, double root x = 3.
Frequently Asked Questions
What does the discriminant tell me?
The discriminant (Δ = b² – 4ac) indicates the number and type of roots. Positive Δ → two distinct real roots. Δ = 0 → one real double root. Negative Δ → two complex conjugate roots. It's the quickest way to understand the solution before calculating the actual values.
Can I use this solver for equations with fractions?
Yes, enter the coefficients as decimal numbers. For example, ½ = 0.5, ⅓ ≈ 0.3333. The solver works with any real number coefficients. For exact fractional results, you may want to use a symbolic algebra tool.