# Rational Root Finder

Learning Tool Last Enhanced on April 6, 2013 at 4:15 am

### The Rational Root Theorem

The rational root theorem states that possible roots for a polynomial can be identified using factors of the constant term (p) and factors of the leading coefficient (q) and take the form of p/q.
For example, suppose the polynomial equation was x2 + 10x + 25 = 0, then p = 25 and q = 1.
Thus factors of p include +/- 1, 5, 25 while factors of q include +/- 1.
The list of all possible rational roots would then be +/- (25/1), (5/1), (1/1).

Using synthetic division, one can quickly determine whether a root is valid.

*A javascript-enabled browser is required to use this tool.

Please select the order of the polynomial:

Then input the coefficients of each term. If a coefficient field is left blank, it is assumed to be ONE (1). Remember to include ZEROES (0) for missing terms and negative signs (-) where a minus appears in your equation. (Currently this only supports integers, fractions and decimals are not allowed). Once you supply the constant term at the end of the equation, a list of factors to determine possible rational roots will appear below.

x10+
x9+
x8+
x7+
x6+
x5+
x4+
x3+
x2+
x1+

Factors of p
Please Supply Coefficients Above
Factors of q
Please Supply Coefficients Above
Possible Rational Roots (p/q)
Please Supply Coefficients Above

*Remember, the factors and possible roots above can be negative (-) or positive (+).

• Pureblood

I am not sure who wrote this up, but it needs to be changed so as not to confuse anyone. p is the factors of the constant term, and q is the factors of the leading coefficient. This page is giving you the reciprocal of the possible roots.