Question

Using the given zero, find one other zero of f(x).

1 - 6i is a zero of f(x) = x4 - 2x3 + 38x2 - 2x + 37

Answer 1

Based on your question where as ask to find the another zero of f(x) 1-6i if 1-6i is root. since complex roots always appears in pairs. the other root must be its conjugate. so the possible value of the other zero is just the same root of the function f(x) and that is 1-6i

Answer 2

`1+6i`

Explanation:

The given function is

`f(x)=x^(4) -2x^(3)+38x^(2) -2x+37`

And the given solution is
`1-6i` which is complex.

To solve this problem, it's important to remember that complex solutions are always in pairs, that is, an equation can't have only 1 complex solution or 3 complex solutions, they must happen in pairs.

Having said that, we know that this function must have 2 complex solution at least, and we already know that one of them is
`1-6i`, which means the second solution is
`1+6i`, because complex solutions happen in conjugates, that's why we know the second one has a positive sign.

Therefore, the other zero for the given function is
`1+6i`.