Find a polynomial of the specified degree that has the given zeros. degree 4; zeros −4, 0, 4, 6

Step-by-step explanation:

1. The polynomial must have the following zeros:

2. This means the following:

3. Multiply each term. The product of the multiplicaction is equal to zero. Then:

4. and are conjugates, therefore, you have:

5. Apply the Distributive property. Then, you obtain:

6. The polynomial of degree 4 and zeros −4, 0, 4 and 6 is:

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i