Polynomial Calculator and Solver

What you can do

• Enter polynomial equations with explicit multiplication and powers.
• Explore supported polynomial solving and analysis through degree eight.
• Review numerical roots alongside equation context rather than relying on one number.
• Use graphing or substitution to verify the sign and location of roots.

Formula and interpretation

A root of a polynomial P(x) is a value r for which P(r) = 0. For a quadratic ax²+bx+c=0, the discriminant b²−4ac indicates whether roots are distinct real values, repeated, or complex. Higher-degree equations may require numerical methods instead of a closed-form expression.

Worked quadratic example

Solve x² − 5x + 6 = 0. Factor the polynomial as (x − 2)(x − 3) = 0, so x = 2 and x = 3. Verify by substitution: 2² − 5×2 + 6 = 0 and 3² − 5×3 + 6 = 0. The solver should agree within numerical tolerance.

How to use the workspace

1. Open Advanced Solver and enter x^2 - 5*x + 6 = 0.
2. Inspect the reported equation type and roots rather than copying unverified output.
3. Substitute each candidate root into the original equation.
4. If a root is approximate, note the residual and required precision.

Assumptions and common errors

• Degree support: the integrated polynomial workflow has documented degree limits; it is not an unlimited symbolic algebra system.
• Extraneous answers: transformations involving denominators or radicals can require checking against the original equation.
• Repeated roots: close numerical roots can be harder to distinguish than well-separated roots.

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