Suppose that a polynomial function of degree 5 with rational coefficients has 6,-3+4i, 4-square root of 3 as zeros. Find the other zeros.

1) 6

2) - 3 + 4i

3) - 3 - 4i

4) 4 - √3

5) 4 + √3

Step-by-step explanation:

A polynomial function of degree 5 means that the highest exponent in this polynomial is 5 and there will be total 5 zeroes or roots.

We are given zeroes of a polynomial,

1) 6

2) - 3 + 4i

3) 4 - √3

Where 6 is the real root, - 3 + 4i is the complex root and 4 - √3 is an irrational root.

The complex roots always exist in conjugate pairs.

-3 + 4i and - 3 - 4i

The irrational roots are also always exist in conjugate pairs.

4 - √3 and 4 + √3

Therefore, all 5 zeroes of the given polynomial function of degree 5 are;

1) 6

2) - 3 + 4i

3) - 3 - 4i

4) 4 - √3

5) 4 + √3