# writing a function given zeros

• August 8th 2008, 12:43 PM
zooanimal98
writing a function given zeros
i have to write a function gven the following zeros:

-1, 2, 3+i, 3-i

i know this: the highest exponent will be to the 4th
the factors are: (x+1), ( x-2), and the other two i am not to sure...

as you can see, i am stuck

can anybody help
• August 8th 2008, 03:34 PM
JaneBennet
$3+\mathrm{i}$ and $3-\mathrm{i}$ are the roots of the equation $x^2-6x+10=0$. (Their sum is 6 and their product is 10.)

Combine this with the linear factors.
• August 8th 2008, 04:21 PM
wingless
How about saying $f = (x+1)(x-2)(x-3-i)(x-3+i)$ ?

Then,

$f = (x+1)(x-2)(x-3-i)(x-3+i)$

$f = (x+1)(x-2)\{[(x-3)-i][(x-3)+i]\}$

$f = (x+1)(x-2)[(x-3)^2+1]$

...