Rational Root Theorem: If p/q (in lowest terms) is a root of a_n*x^n + ... + a_0 = 0 with integer coefficients, then p divides a_0 and q divides a_n.

Application: For x^2 + bx + c = 0 with integer coefficients (leading coeff 1), any rational root must be an integer dividing c. This narrows the search dramatically.

For JEE: When a problem asks "find integer roots" or "find rational roots," use this theorem to list candidates, then verify by substitution.