Suppose a polynomial function of degree 5 with rational coef

Suppose a polynomial function of degree 5 with rational coefficients has the given numbers as zeros. Find the other zero. 1, 5, 5 -5i, 5 The other zero is _________.

Solution

Extremely easy

Just as irrational roots appear in pairs,
so to do complex roots

So, if 5 - 5i is a root,
then 5 + 5i is also

And with that, we have our five roots :
1 , 4 , 5 - 5i , 5 + 5i and another 5

So, the other zero is :
5 + 5i