Question

To create a fourth degree polynomial function that has zeros -5i and 6 and opens upwards?

Answer 1

To create a fourth degree polynomial function that has zeros -5i and 6 and opens upwards, we can use the fact that complex roots occur in conjugate pairs.

Step-by-step explanation:

To create a fourth degree polynomial function that has zeros -5i and 6 and opens upwards, we can use the fact that complex roots occur in conjugate pairs. Since -5i is a root, its conjugate 5i is also a root.

Therefore, the quadratic factors of the polynomial are (x + 5i) and (x - 5i).

The linear factors of the polynomial are (x - 6), (x + 6), and (x - 5i), (x + 5i).

Multiplying all these factors together, we get the fourth degree polynomial function: f(x) = (x - 6)(x + 6)(x - 5i)(x + 5i).