Apply the Fundamental Theorem of Algebra to find the number of imaginary roots for the polynomial f(x)=4x^2−14+x^8 , if you know its graph has two x-intercepts.(1 point)
The Fundamental Theorem of Algebra states that a polynomial of degree n will have exactly n complex roots. In this case, the degree of the polynomial f(x) = 4x^2 - 14 + x^8 is 8. Since the graph of the polynomial has 2 x-intercepts, it means that it has 2 real roots.
Therefore, according to the Fundamental Theorem of Algebra, the remaining roots must be complex roots. Thus, the number of imaginary roots for the polynomial f(x) = 4x^2 - 14 + x^8 is 8 - 2 = 6.