Question

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

2 - 4i is a zero of f(x).= x4 - 4x3 + 21x2 - 4x + 20

I'm not sure how to solve this :\

Answer 1

complex root always come in pairs:a-bi and a+bi.
Since \(2-4i\) is a zero, then \(2+4i\) as well. So \((x-(2-4i))(x-(2+4i))=(x-2)^2+16\) is a factor of \(f(x)\). Next divide \(f(x)\) by \((x-2)^2+16=x^2-4x+20\) using long division. You got a quotient which is quadratic, and you can find its zeros by quadratic formula