Question

What are the possible rational roots of the polynomial equation 0 = 3x⁸ + 11x⁵ + 4x + 6?

A) 0, 1, -1, 1/3, -1/3, 2/3, -2/3
B) 0, 1, -1, 2, -2, 3, -3
C) 0, 1, -1, 4, -4, 6, -6
D) 0, 1, -1, 1/2, -1/2, 1/4, -1/4

Answer 1

The possible rational roots of the polynomial equation 0 = 3x⁸ + 11x⁵ + 4x + 6 are 0, 1, -1, 1/3, -1/3, 2/3, and -2/3.

Step-by-step explanation:

The possible rational roots of the polynomial equation 0 = 3x⁸ + 11x⁵ + 4x + 6 can be found using the Rational Root Theorem. According to the theorem, the possible rational roots are of the form p/q, where p is a factor of the constant term (in this case, 6) and q is a factor of the leading coefficient (in this case, 3). Knowing this, we can narrow down the options and determine that the possible rational roots are 0, 1, -1, 1/3, -1/3, 2/3, and -2/3.