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 have always been a friend to hero-worship; it is the only rational one, and has always been in use amongst civilized people—the worship of spirits is synonymous with barbarism—it is mere fetish.... There is something philosophic in the worship of the heroes of the human race.”
—George Borrow (1803–1881)
“To those who despair of everything reason cannot provide a faith, but only passion, and in this case it must be the same passion that lay at the root of the despair, namely humiliation and hatred.”
—Albert Camus (1913–1960)
“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)