Question

Find the rational roots of x^4 + 3x^3 + 3x^2 - 3x - 4 = 0
0, 1
1, 2
1, -1
-1, 2

Answer 1

To find the rational roots of the polynomial, we can use the Rational Root Theorem. The Rational Root Theorem states that if the polynomial has a rational root (a/b), where a is a factor of the constant term and b is a factor of the leading coefficient, then a possible rational root is ±a/b.

For the polynomial x^4 + 3x^3 + 3x^2 - 3x - 4 = 0, the constant term is -4 and the leading coefficient is 1. The factors of -4 are ±1, ±2, ±4, and the factors of 1 are ±1.

So, the possible rational roots are ±1, ±2, and ±4.

By testing these roots, we find that the polynomial has rational roots x = -1 and x = 1.

Therefore, the rational roots of x^4 + 3x^3 + 3x^2 - 3x - 4 = 0 are x = -1 and x = 1.