Rational Root Theorem

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:

    So far as discipline is concerned, freedom means not its absence but the use of higher and more rational forms as contrasted with those that are lower or less rational.
    Charles Horton Cooley (1864–1929)

    Black creeps from root to root,
    each leaf
    cuts another leaf on the grass,
    shadow seeks shadow,
    then both leaf
    and leaf-shadow are lost.
    Hilda Doolittle (1886–1961)

    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 (1913–1960)