Question

Is relation root theorem asked to be proven in board exams?

Answer 1

In algebra, the rational root theorem (or rational root test, rational zero theorem, rational zero test or p/q theorem) states a constraint on rational solutions of a polynomial equation

with integer coefficients. Solutions of the equation are roots (equivalently, zeroes) of the polynomial on the left side of the equation.

If a0 and an are nonzero, then each rationalsolution x, when written as a fraction x = p/qin lowest terms (i.e., the greatest common divisor of p and q is 1), satisfies

p is an integer factor of the constant terma0, and

q is an integer factor of the leading coefficient an.

The rational root theorem is a special case (for a single linear factor) of Gauss's lemmaon the factorization of polynomials. The integral root theorem is a special case of the rational root theorem if the leading coefficient an = 1.