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December 20, 2014

December 20, 2014

Posted by **Emily** on Sunday, September 20, 2009 at 10:51pm.

I used synthetic division to get the real roots 2 and -1, but I can't figure out how to get the imaginary roots. I checked HotMath but all it showed me was how to get the real roots and then it practically gave me the imaginary roots without showing how to work it out. Does anyone know how to do this? Any help is GREATLY appreciated!! :D

- Precalculus -
**Reiny**, Sunday, September 20, 2009 at 11:01pmhow about this

let y = x^3

then your equation becomes

y^2 - 7y - 8 = 0

(y-8)(y+1) = 0

so y = 8 or y = -1

then x^3 = 8 or x^3 = -1

x^3 - 8 = 0

(x-2)(x^2 + 2x + 4) = 0

this will give you the real root of x=2 and 2 imaginary roots from the quadratic

or

x^3 + 1 = 0

(x+1)(x^2 - x + 1) = 0

here x = -1 plus 2 more imaginary roots

- Precalculus -
**Emily**, Sunday, September 20, 2009 at 11:07pmOhhhh duh!! I can't believe I totally overlooked that. Thanks Reiny!! :D

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