3rd degree polynomials?

[emily.]

If the function f(x) is a 3rd degree function and has one zero 1+2i, how many real zeroes does it have?


WHAT? Can someone please explain this to me and how to solve it? THANKS.

 

[Mrspi]

If the function f(x) is a 3rd degree function and has one real zero 1+2i, how many real zeroes does it have?


WHAT? Can someone please explain this to me and how to solve it? THANKS.

1 + 2i is NOT a real number.

I suspect that you are told that ONE of the zeros of the function f(x) is 1 + 2i.

1 + 2i is a complex number, and complex zeros always occur in conjugate pairs. So, if 1 + 2i is a zero of the function, then 1 - 2i is also a zero of the function.

A function of degree 3 has THREE zeroes. If two of them are complex (and we know that 1 + 2i and 1 - 2i are zeroes), then the remaining zero must be real.

Hint for checking....what does the graph of the GENERAL third degree function look like? f(x) = x³


You might find this web page instructive:

http://en.wikipedia.org/wiki/Cubic_function