In algebra, the rational root theorem (or rational root test) states a constraint on rational solutions (or roots) of the polynomial equation
with integer coefficients.
If a0 and an are nonzero, then each rational solution x, when written as a fraction x = p/q in lowest terms (i.e., the greatest common divisor of p and q is 1), satisfies
- p is an integer factor of the constant term a0, and
- q is an integer factor of the leading coefficient an.
Thus, a list of possible rational roots of the equation can be derived using the formula .
The rational root theorem is a special case (for a single linear factor) of Gauss's lemma on the factorization of polynomials. The integral root theorem is a special case of the rational root theorem if the leading coefficient an = 1.
Read more about Rational Root Theorem: Example
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