Question

x^2+2ix+3=0
find the polynomials

Answer 1

I am not sure if I understand this question correctly @kalemale, you search the solution for this polynomial and then you want to factor it?

Answer 2

I dont know either I did not get a root in my book so I dont really know how to solve

Answer 3

Because in this case you could just solve the quadratic equation using the laws of complex numbers and you will find that the two purely imaginary roots

\[ x=i \\ x=-3i \]
So your polynomial would be \[(x-i)(x+3i)=x^2+2ix+3\]

Answer 4

hmm thanks how I know when I can use it to solve theese kinds of problems?

Answer 5

whenever you have a polynomial in quadratic form (the leading term is x^2) you can use the formula for solving the quadratic equation.

\[ \frac{-b \pm \sqrt{b^2-4ac}}{2a}\]

if
\[ D=b^2-4ac < 0 \] you have to use the arguments for complex numbers

\[ i^2 = -1 \longrightarrow i = \sqrt{-1}\]

Answer 6

I hope this helps, if you have further questions, I will be back in a few.

Answer 7

Good luck! (-;

Answer 8

Thanks alot !!! =)