SOLUTION: what is exact value of the only real root of the equation x^3 + 6x^2 + 12x + 24 = 0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: what is exact value of the only real root of the equation x^3 + 6x^2 + 12x + 24 = 0      Log On


   

Question 574550: what is exact value of the only real root of the equation x^3 + 6x^2 + 12x + 24 = 0
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
When you look at x%5E3+%2B+6x%5E2+%2B+12x+%2B+24+=+0, it may remind you of
%28x%2B2%29%5E3=x%5E3%2B6x%5E2%2B12x%2B8, so we could "complete the cube"
x%5E3+%2B+6x%5E2+%2B+12x+%2B+24+=+0 --> x%5E3+%2B+6x%5E2+%2B+12x+=+-24 --> x%5E3+%2B+6x%5E2+%2B+12x+%2B8=+-24%2B8 --> %28x%2B2%29%5E3=-16
The only real solution is x%2B2=root%283%2C16%29 , so
highlight%28x=-2-root%283%2C16%29%29