Calculatrice de Racines de Polynôme Gratuite
Trouvez les racines d'un polynôme. Calculez les zéros réels et complexes de polynômes de degré 2, 3 ou supérieur.
Sum Roots
6.0000
Formule
Polynomial Roots via Vieta's Formulas
For a Cubic ax³ + bx² + cx + d = 0
Vieta's formulas relate the roots (r₁, r₂, r₃) to the coefficients:
Discriminant
The discriminant tells you about the nature of the roots:
Exemple Résolu
Analyze x³ - 6x² + 11x - 6 = 0 (roots are 1, 2, 3).
- 01Sum of roots = -(-6)/1 = 6 (= 1+2+3)
- 02Sum of pairwise products = 11/1 = 11 (= 1×2+1×3+2×3)
- 03Product of roots = -(-6)/1 = 6 (= 1×2×3)
Questions Fréquentes
What are Vieta's formulas?
Vieta's formulas express relationships between the coefficients of a polynomial and sums and products of its roots, without needing to find the roots explicitly.
Can this find the actual roots?
This calculator shows the sum and product of roots via Vieta's formulas. For exact roots, factoring or numerical methods are typically needed for cubics and higher.
What does the discriminant indicate?
A positive discriminant means three distinct real roots. Zero means at least one repeated root. Negative means one real root and two complex conjugate roots.
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