algebra 2 question

Question

Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 5; zeros 5; -i; 8+i

 

so what is the polynomial f(x) =a?

Answer 1

Since the degree is 5, we will have 5 zeros.  Or we can say 5 factors multiplied together.  The first term when expanded out is Cx⁵.  C is a constant.

 

 

We are given 3 zeros, so we can use the conjugates of the complex zeros to get the last two zeros.  These last two zeros are:

 

i, and (8 - i)

 

 

So the polynomial you want is:

 

f(x) = (x - 5)(x - i)(x + i)(x - 8 - i)(x - 8 + i)