Question

How do you find the complex roots of a polynomial?

Answer 1

Do you have an example? The process could be different depending on what you have.

Answer 2

4x^3 – 12x + 9 = 0
Something like this... The example my teacher gave to me said that because equation has a degree of 3 it has 3 complex roots... and i think im interpreting that wrong

Answer 3

Its impossible to have 3 complex roots. There can only be an even number of roots.

Answer 4

even number of complex I mean

Answer 5

he said that for imaginary roots

Answer 6

Yeah, complex roots and imaginary roots you can consider to be the same thing. There must be an even number of imaginary roots. So this cubic either has 2 imaginary roots or 0.

Answer 7

okay so it can be either one? or do i have to find out which one?

Answer 8

Yes, you might have 2 imaginary or you might have 0 imaginary. You would want to ty and see if you could factor the cubic and find its zeros first.

Answer 9

Okay! Thanks for clearing that up for me!

Answer 10

Mhm, sure. If you had to actually do this problem, though, it appears that it wont factor cleanly. The best you could do is show that it does have 1 real zero and that there cant be another real zero. So yeah, this problem has 2 imaginary roots.

Answer 11

Thanks!

Answer 12

No problem