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:
“While the miser is merely a capitalist gone mad, the capitalist is a rational miser.”
—Karl Marx (1818–1883)
“Perhaps the whole root of our trouble, the human trouble, is that we will sacrifice all the beauty of our lives, will imprison ourselves in totems, taboos, crosses, blood sacrifices, steeples, mosques, races, armies, flags, nations, in order to deny the fact of death, which is the only fact we have.”
—James Baldwin (1924–1987)
“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)