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Quadratic equation solver
Solve ax² + bx + c = 0 with discriminant and roots.
Roots
x = 2 | 1
Two real roots
What do these numbers mean?
- Roots are x values that make ax² + bx + c equal zero. A positive discriminant gives two real roots, zero a repeated root, and negative complex roots. In complex results, i² = −1.
- In decimal numbers, commas separate thousands and a dot separates decimals: 1,234.5 = 1234 + 0.5. ×10^3 means multiply by 1000; ×10^-3 means divide by 1000. Display rounding can make tiny differences between shown totals.
| x₁ | 2 |
| x₂ | 1 |
| Sum / product | 3 / 2 |
| Vertex x-coordinate | 1.5 |
Curve y = ax² + bx + c
How this is worked out
- Discriminant: -3² − 4×1×2 = 1.
- x = (−b ± √Δ) ÷ 2a = 2 and 1.
Real roots for a nonnegative discriminant; complex roots otherwise. If a = 0, the linear case is used.