The Fundamental Theorem of Algebra states that a polynomial of degree n has exactly n complex roots, counting multiplicity.
In this case, the polynomial f(x) = 4x^2 - 14 + x^8 has a degree of 8 because of the highest power of x, which is x^8.
Since we know from the given information that the graph of f(x) has two x-intercepts, we can conclude that the polynomial has exactly 2 real roots.
By applying the Fundamental Theorem of Algebra, the remaining roots must be complex roots.
Therefore, the number of imaginary roots for the polynomial f(x) = 4x^2 - 14 + x^8 is 8 - 2 = 6.
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.
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