Find Polynomial given zeros

**aikenfan** · September 28th 2007, 01:17 PM

I get this far, and then i get stuck..i dont know what to do...when I multiply by (X + 8i), i keep getting the wrong answer..could someone please help me? Thank you

**Plato** · September 28th 2007, 01:22 PM

If you want all real coefficients, then the complex roots must occur in conjugate pairs.
So use {-3,4,8i,-8i} four roots give four factors.

**aikenfan** · September 28th 2007, 01:28 PM

Now I get
x^2 - x - 12 (x^2 - 64i^2)
Now do I multiply those together?

**Plato** · September 28th 2007, 01:57 PM

$\left( {x^2 - x - 12} \right)\left( {x^2 + 64} \right) =$ $\left( {x^2 } \right)\left( {x^2 } \right) + \left( {x^2 } \right)\left( {64} \right) + \left( { - x} \right)\left( {x^2 } \right) + \left( { - x} \right)\left( {64} \right) + \left( { - 12} \right)\left( {x^2 } \right) + \left( { - 12} \right)\left( {64} \right)<br />$

**aikenfan** · September 28th 2007, 02:07 PM

x^4 - x^3 + 52x^2 - 768

**Plato** · September 28th 2007, 02:32 PM

Originally Posted by aikenfan

x^4 - x^3 + 52x^2 - 768

You missed a term.
x^4 - x^3 + 52x^2 -64x - 768

**aikenfan** · September 28th 2007, 02:59 PM

Thank you for all of your help

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