The degree of a polynomial is determined by the total number of roots it has, counting both real and imaginary roots.
You mentioned that the polynomial has:
- Two x-intercepts (real roots), and
- Four imaginary roots.
Imaginary roots come in conjugate pairs, so if there are four imaginary roots, that means there are two pairs of complex conjugates.
Adding these together:
- 2 real roots (from the x-intercepts)
- 4 imaginary roots (which can be counted as 4 roots)
Thus, the total number of roots is \(2 + 4 = 6\).
Therefore, the degree of the polynomial must be 6.
The correct answer is: 6.
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