### Need help from an expert?

The world’s top online tutoring provider trusted by students, parents, and schools globally.

The rational root theorem is a method for finding possible rational roots of a polynomial equation.

The rational root theorem states that if a polynomial equation with integer coefficients has a rational root, then that root must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. This means that the possible rational roots of a polynomial equation can be found by listing all the factors of the constant term and all the factors of the leading coefficient, and then forming all possible fractions using one factor from each list.

For example, consider the polynomial equation 2x^3 + 5x^2 - 3x - 2 = 0. The constant term is -2, which has factors of ±1 and ±2. The leading coefficient is 2, which has factors of ±1 and ±2. Therefore, the possible rational roots of the equation are ±1/1, ±1/2, ±2/1, and ±2/2, which simplify to ±1, ±1/2, ±2, and ±1.

To use the rational root theorem to solve a polynomial equation, we can test each of the possible rational roots by substituting them into the equation and checking if the result is zero. If we find a root that works, we can use polynomial division to factor the equation and find the other roots. If none of the possible rational roots work, we may need to use other methods, such as the quadratic formula or numerical methods, to find the roots.

Study and Practice for Free

Trusted by 100,000+ Students Worldwide

Achieve Top Grades in your Exams with our Free Resources.

Practice Questions, Study Notes, and Past Exam Papers for all Subjects!

The world’s top online tutoring provider trusted by students, parents, and schools globally.

Loading...

Loading...