# Thread: Find Polynomial given zeros

1. ## Find Polynomial given zeros

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

2. 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.

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

4. $\left( {x^2 - x - 12} \right)\left( {x^2 + 64} \right) =$ $\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)
$

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

6. Originally Posted by aikenfan
x^4 - x^3 + 52x^2 - 768
You missed a term.
x^4 - x^3 + 52x^2 -64x - 768

7. Thank you for all of your help