Question

Using the rational root theorem, list out the potential rational roots for the polynomial f(x)=11x^(3)-14+x-2x^(4)+17x^(2).

Answer 1

The potential rational roots for the given polynomial equation are 1/1, 1/2, 2/1, 2/2, -1/1, -1/2, -2/1, and -2/2.

Step-by-step explanation:

The rational root theorem states that if a polynomial equation has a rational root, then that root will be a factor of the constant term divided by a factor of the leading coefficient.

In this case, the constant term is -2 and the leading coefficient is -2. Therefore, the potential rational roots for the polynomial f(x)=11x^3-14x-2x^4+17x^2 are the factors of -2 divided by the factors of -2.

The factors of -2 are 1 and 2, and the factors of -2 are 1 and 2. So, the potential rational roots are 1/1, 1/2, 2/1, 2/2, -1/1, -1/2, -2/1, and -2/2.