# Find Polynomial given zeros

• Sep 28th 2007, 01:17 PM
aikenfan
Find Polynomial given zeros
http://i103.photobucket.com/albums/m...9/111001-2.jpg
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
• Sep 28th 2007, 01:22 PM
Plato
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.
• Sep 28th 2007, 01:28 PM
aikenfan
Now I get
x^2 - x - 12 (x^2 - 64i^2)
Now do I multiply those together?
• Sep 28th 2007, 01:57 PM
Plato
$\left( {x^2 - x - 12} \right)\left( {x^2 + 64} \right) =$ $\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)
$
• Sep 28th 2007, 02:07 PM
aikenfan
x^4 - x^3 + 52x^2 - 768
• Sep 28th 2007, 02:32 PM
Plato
Quote:

Originally Posted by aikenfan
x^4 - x^3 + 52x^2 - 768

You missed a term.
x^4 - x^3 + 52x^2 -64x - 768
• Sep 28th 2007, 02:59 PM
aikenfan
Thank you for all of your help:)