Apply the fundamental theorem of Algebra to find the number of roots for the equation 12−6x3+3x4=6x3+2x+x5 (1 point) Responses 2 2 3 3 4 4 5
The fundamental theorem of Algebra states that a polynomial equation of degree n has exactly n roots, counting multiplicities.
In this case, the equation 12−6x^3+3x^4=6x^3+2x+x^5 is a polynomial equation of degree 5. Therefore, it has exactly 5 roots.
So, the correct response is 5.