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.