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
Famous quotes containing the words rational, root and/or theorem:
“[I]n Great-Britain it is said that their constitution relies on the house of commons for honesty, and the lords for wisdom; which would be a rational reliance if honesty were to be bought with money, and if wisdom were hereditary.”
—Thomas Jefferson (17431826)
“Propaganda has a bad name, but its root meaning is simply to disseminate through a medium, and all writing therefore is propaganda for something. Its a seeding of the self in the consciousness of others.”
—Elizabeth Drew (18871965)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (19131960)