Apply the Fundamental Theorem of Algebra to find the number of imaginary roots for the polynomial f(x)=4x2−14+x8
, if you know its graph has two x-intercepts.(1 point)
imaginary roots
The Fundamental Theorem of Algebra states that a polynomial of degree n has exactly n complex roots, counting multiplicities.
In this case, the polynomial f(x) = 4x^2 - 14 + x^8 has a degree of 8. Since the graph of the polynomial has two x-intercepts, this means that it has two real roots.
Therefore, the remaining 8-2=6 roots must be imaginary. So, we can conclude that f(x) has 6 imaginary roots.