use the following zeros to write a polynomial function

Question

1. 3,2+√5

2. 4,1+√5

3. 2,2i,4-√6

4.3,3-i

 

Answer 1

I will do one of these for you and explain how you should do the rest.

First of all, I think this problem assumes that the polynomial requested has rational coefficients, even though it does not say so.

 

In that situation, complex roots and quadratic surds occur is conjugate pairs, i.e. if a + √b is a root, so is a - √b; likewise if

a+ bi is a root, so is a - bi.

 

Look at the 3rd problem:

The roots are 2, 2i, -2i, 4-√6 and 4 + √6

The equation then is a 5th degree polynomial as follows: (x² - 4)(x² + 8x + 10)(x -2)

You can do the multiplications to get the specific polynomial.

 

You work the other problems in exactly the same way.