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Quadratic & polynomial equations formulas
14 formulas for Quadratic & polynomial equations, from the Algebra section of the Quantix formula library. Tap 🧮 next to a formula to solve it for any variable with step-by-step working.
| Name | Formula | Note |
|---|---|---|
| Quadratic formula | x = (−b ± √(b² − 4ac)) / 2a | ax² + bx + c = 0 |
| Discriminant | D = b² − 4ac 🧮 Solve step by step | D > 0 two real, D = 0 equal, D < 0 complex roots |
| Sum of roots | α + β = −b / a 🧮 Solve step by step | |
| Product of roots | αβ = c / a 🧮 Solve step by step | |
| Equation from roots | x² − (α + β)x + αβ = 0 🧮 Solve step by step | |
| Difference of roots | |α − β| = √D / |a| | |
| α² + β² | (α + β)² − 2αβ | |
| α³ + β³ | (α + β)³ − 3αβ(α + β) | |
| Vertex of parabola | x = −b / 2a, y = −D / 4a 🧮 Solve step by step | |
| Cubic — sum of roots | α + β + γ = −b/a 🧮 Solve step by step | ax³ + bx² + cx + d = 0 |
| Cubic — pair products | αβ + βγ + γα = c/a 🧮 Solve step by step | |
| Cubic — product | αβγ = −d/a 🧮 Solve step by step | |
| Remainder theorem | Remainder of p(x) ÷ (x − a) = p(a) | |
| Factor theorem | (x − a) is a factor ⇔ p(a) = 0 |
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