Loading...

Polynomial Roots Calculator

Find the real roots of quadratic (degree 2) or cubic (degree 3) polynomials. Enter coefficients separated by commas.

Math

Share

Coefficients (constant to highest)

Formula

Find the real roots of a polynomial. Supports quadratic (ax²+bx+c) and cubic (ax³+bx²+cx+d) polynomials. Enter coefficients from constant term to highest degree.

Solve P(x) = 0

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter coefficients separated by commas (constant term first, highest degree last).
2Click Calculate to find real roots.
3For cubic equations, one real root is found via Cardano's formula.

Examples

Find roots of x² − 3x + 2

1.Enter 2,-3,1 (constant=2, x=-3, x²=1).
2.Discriminant = 9 − 8 = 1.
3.Roots: (3 ± 1)/2 = 2 and 1.
4.Result: 2, 1.

Result: 2.0000, 1.0000

Find roots of x³ − 6x² + 11x − 6

1.Enter -6,11,-6,1.
2.Cardano's formula finds one real root.
3.Result: 1.

Result: 1.0000

Frequently Asked Questions

Quadratic (degree 2) finds up to 2 real roots. Cubic (degree 3) finds one real root via Cardano's formula.

No, only real roots are displayed. If the discriminant is negative for quadratics, no real roots are reported.

From constant term to highest degree. For 2x²−3x+1 enter 1,-3,2. For x³−2x+1 enter 1,-2,0,1.

If the polynomial has no real roots, the result shows 'No real roots found'.

Use the Polynomial Calculator for evaluation. This calculator only finds roots.

Related Calculators

Polynomial Calculator Factoring Calculator Equation Solver Cubic Equation Calculator Percentage Calculator Basic Calculator

CalculateMe Team

Last updated: 2026-07-13

Polynomial Roots Calculator - Find Roots of Polynomial | CalculateMe | CalculateMe