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

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- Aug 8th 2008, 12:43 PMzooanimal98writing 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 - Aug 8th 2008, 03:34 PMJaneBennet
$\displaystyle 3+\mathrm{i}$ and $\displaystyle 3-\mathrm{i}$ are the roots of the equation $\displaystyle x^2-6x+10=0$. (Their sum is 6 and their product is 10.)

Combine this with the linear factors. - Aug 8th 2008, 04:21 PMwingless
How about saying $\displaystyle f = (x+1)(x-2)(x-3-i)(x-3+i)$ ?

Then,

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

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

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

...