CalculateMeasure

Math & Geometry

Polynomial Roots Calculator

Find the roots of a linear, quadratic, or cubic polynomial by entering coefficients for ax³ + bx² + cx + d = 0.

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Calculator guide

How to use the Polynomial Roots Calculator

Find the roots of a linear, quadratic, or cubic polynomial by entering coefficients for ax³ + bx² + cx + d = 0. Enter the requested values and select Calculate. The result and supporting values are produced locally in your browser.

Formula

Solve ax³ + bx² + cx + d = 0 (falls back to quadratic or linear when leading coefficients are zero)

Worked example

For x³ − 6x² + 11x − 6 = 0, the roots are 1, 2, and 3.

What to keep in mind

  • This calculator supports real-coefficient polynomials through degree 3.
  • Complex roots are shown with i when they occur.

Methodology

This calculator uses deterministic arithmetic and performs the calculation locally in your browser. Verify assumptions, units, and source values for your specific use case.

Review standard: Level A · Standard formula. How calculator reviews work.

Frequently asked questions

What does this calculator calculate?

Find the roots of a linear, quadratic, or cubic polynomial by entering coefficients for ax³ + bx² + cx + d = 0.

How is the result calculated?

Solve ax³ + bx² + cx + d = 0 (falls back to quadratic or linear when leading coefficients are zero).

Can I use the result for an important decision?

Use the result as a calculation aid and verify the inputs, assumptions, and applicable professional or regulatory requirements before relying on it for an important decision.

Does CalculateMeasure store the values I enter?

The calculator performs its arithmetic in your browser. The calculator itself does not need to send your entered values to a server to produce the result.