Question

Apply the Fundamental Theorem of Algebra to find the number of roots for the equation 12x−6x2+3x4=6x3+2x−x4
.(1 point)
Responses

4
4

3
3

1
1

2

Answer 1

Rearrange to one side:
4x^4 − 6x^3 − 6x^2 + 10x = 0 (factor: 2x(2x^3 − 3x^2 − 3x + 5) = 0).

This is a degree-4 polynomial, so by the Fundamental Theorem of Algebra it has 4 roots (counting multiplicity, in the complex numbers).