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

"Show that x^6 - 7x^3 - 8 = 0 has a quadratic form. Then find the two real roots and the four imaginary roots of this equation."

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 11:01pm
how 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 11:07pm
Ohhhh duh!! I can't believe I totally overlooked that. Thanks Reiny!! :D

## Answer this Question

## Related Questions

- Alg II - I'm working with finding roots of polynomial equations with degrees of ...
- Alg II - I'm working with finding roots of polynomial equations with degrees of ...
- algebra - if a quadratic equation with real coefficents has a discriminant of 10...
- Algebra II - Which describes the number and type of roots of the equation x^2 -...
- maths2 - Use the discriminant to determine the number of real roots the equation...
- mathematics - Use the discriminant to determine the number of real roots the ...
- Math - Which describes the number and type of roots of the equation x^2-625=0? A...
- Pre Calc (For Reiny) - Thanks so much your method worked perfectly! My solution ...
- Pre-Calc/Trig... - Helpp needed, this is sort of confusing me. Describe the ...
- Alegbra - I need help, my teacher says that I'm half way right with this but ...