# Thread: Polynom with real coeff

1. ## Polynom with real coeff

Hi guys,
I need to create a polynomial with real coefficients that has the roots $\displaystyle 3,1, and -i$. Then multiply and simplify.

So far I have done this:

$\displaystyle (x-3)(x-1)= (x^{2}-4x+3)$

I know that $\displaystyle -i= \sqrt{-1}$

2. hi
$\displaystyle \left ( x-1 \right )\left ( x-3 \right )\left ( x^{2}+1 \right )$ = $\displaystyle {x}^{4}-4\,{x}^{3}+4\,{x}^{2}-4\,x+3$,this polynomial has four roots $\displaystyle -i,i,1,3$.

3. Originally Posted by wykamikaam
Hi guys,
I need to create a polynomial with real coefficients that has the roots $\displaystyle 3,1, and -i$. Then multiply and simplify.

So far I have done this:

$\displaystyle (x-3)(x-1)= (x^{2}-4x+3)$
If -i is a root, then so is i (complex conjugates). So your polynomial would be
$\displaystyle (x - 3)(x - 1)(x - i)(x + i)$.

Multiply it out to get your answer. (Note that $\displaystyle (x - i)(x + i) = x^2 + 1$.)

01

EDIT: Roah beat me to it...

4. Thanks a lot to both of you!