List all the possible rational solutions of 3x^4-2x^3+11x-1=0.

Answer 1

This is an application of the Rational Root Theorem.

Any irreducible rational root of a polynomial is of the form

±p/q

where p and q are relatively prime positive integers with the property:

1. p must be a divisor of the constant coefficient, which in your case is 1.

So the only possibility is p = 1.

2. q must be a divisor of the highest-order coefficient, which in your case is 3.

So you have two options for q -- q = 1 or q = 3.

In total there are only four candidates for rational coefficients of the equations:

1/1, 1/3, -1/1, -1/3

You can plug them into the equation to see if any of them is a root.