What must be the degree of a polynomial function with two x-intercepts and four imaginary roots?(1 point)

Responses

8
8

2
2

4
4

6

1 answer

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.