Rational Root Theorem

Rational Root Theorem
Rational Zero Theorem

A theorem that provides a complete list of possible rational roots of the polynomial equation a_nxⁿ + a_n_–1xⁿ^–1 + ··· + a₂x² + a₁x + a₀ = 0 where all coefficients are integers.

This list consists of all possible numbers of the form c/d, where c and d are integers. c must divide evenly into the constant term a₀. d must divide evenly into the leading coefficient a_n.

Example applying Rational Root Theorem to 6x⁴−2x³+5x²+x−10=0; p=±1,±2,±5,±10; q=±1,±2,±3,±6; lists possible zeros p/q.

See also

Polynomial facts