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

Question

Responses

8
8

4
4

2
2

6

Answer 1

The degree of a polynomial is equal to the sum of the number of real roots and the number of imaginary (complex) roots.

In this case, the polynomial has:

• 2 real roots (the x-intercepts)
• 4 imaginary roots

Imaginary roots typically come in conjugate pairs; hence, 4 imaginary roots would mean there are 2 pairs of conjugates (2 + 2 = 4).

Now we can calculate the total degree of the polynomial:

• 2 real roots + 4 imaginary roots = 6

Thus, the degree of the polynomial must be 6.

So the correct response is 6.