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

4 - 5i is a zero of f(x).= x^4 - 8x^3 + 42x^2 - 8x + 41.

Question

Using the given zero, find one other zero of f(x).

4 - 5i is a zero of f(x).= x^4 - 8x^3 + 42x^2 - 8x + 41.

anonymous · Answer

one zero is $4-5i$ so the other zero must be the conjugate $4+5i$
now we can figure out what that polynomial must be fairly easily

anonymous · Answer

Oh okay so it's just the conjugate. Thank you.

anonymous · Answer

one way is to work backwards
$$x=4-5i\x-4=-5i\(x-4)^2=-25\x^2-8x=-25\x^2-8x+25=0$$

anonymous · Answer

oh you only have to find ONE other zero?  then it is really easy, just the conjugate
i thought you had to find all of them!

anonymous · Answer

helps if i would read the question ....