Find a polynomial P(x) with integer coefficients that satisfy the following conditions:
P(x) has degree 4 with the zeros 3, 0 and -i

Question

Find a polynomial P(x) with integer coefficients that satisfy the following conditions:
P(x) has degree 4 with the zeros 3, 0 and -i

mertsj · Answer

The roots come in complex conjugates so is -i is a root, so is i.  Therefore the factors are:  P(x)= (x-0)(x-3)(x-i)(x+i)

mertsj · Answer

You could multiply it out if you want a different form.

didee · Answer

Hi, thanks. Ok, they say -i is a root but they don't say i is a root, same with -3. This is what throws me out.

anonymous · Answer

-3 is a root doesn't give you additional information, but complex roots come in conjugate pairs, so if $a+bi$ is a root so is $a-bi$

didee · Answer

Thanks so much

anonymous · Answer

btw i hope it is easy to multiply $(x+i)(x-i)$ you get $x^2+1$ pretty much instantly
yw

didee · Answer

Yes I figured, thanks :-)