What is the rational zero theorem?

The rational zero theorem is a theorem in algebra that helps to find the possible rational roots or zeros of a polynomial equation.

It states that if a polynomial equation has integer coefficients, then any rational zero of the equation must be of the form of a fraction, in which the numerator is a factor of the constant term of the polynomial, and the denominator is a factor of the leading coefficient.

This theorem can be used in finding all the rational roots or zeros of a polynomial equation and reducing the degree of the equation before using other methods of solving the equation. It can also help in verifying whether a particular number is a zero of the given polynomial or not.

However, it should be noted that this theorem only helps in finding the rational roots, and it does not guarantee that the polynomial has any rational roots. If the rational zero theorem fails to find any rational roots, then other methods such as the quadratic formula or the factor theorem can be used.