Using the given zero, find one other zero of f(x).
i is a zero of f(x)= x^4 - 2x^3 + 38x^2 - 2x + 37.

Question

Using the given zero, find one other zero of f(x).
i is a zero of f(x)= x^4 - 2x^3 + 38x^2 - 2x + 37.

anonymous · Answer

divide the function by the equation of the zero.

anonymous · Answer

What equation of the zero???

anonymous · Answer

what is your zero?

anonymous · Answer

That's the whole question. It only gave me i as one of the zeros.

anonymous · Answer

i? i is not a zero

anonymous · Answer

It's one of the zeros of that equation.

anonymous · Answer

i is a variable, it can't be a zero

anonymous · Answer

It's just an imaginary one I guess. No, it's not a variable, this means i as in, like on a calculator.. the mathematical symbol..

phi · Answer

this one ?

anonymous · Answer

Yesh.

phi · Answer

if you have a function that is a polynomial with real  coefficients,
then its complex roots (if any) come in complex conjugate pairs.

phi · Answer

the complex conjugate of a+ bi  is a-bi

in your case, a=0, b=1

phi · Answer

btw, i is short for $$ \sqrt{-1} $$

anonymous · Answer

I remember that now, about i. But how do I figure out the other zeros??

phi · Answer

the question asks for one other, so x= -i sounds good enough
but if you want the other 2 (you do know you should get 4 zeros, right? because the highest order term is x^4)

you could multiply out (x-i)(x+i)
and get a real polynomial.  it will divide evenly into the original (because both x-i and x+i are factors)

you will get a quadratic that you can solve using the quadratic formula

anonymous · Answer

Okay, awesome. Thanks!