Question 49184: according to descartes rule of signs,(a) how many positive roots does this equation have ?
(b)how many negative roots? f(x)=3x^3+9x^2+8x
Answer by Nate(3500)   (Show Source):
You can put this solution on YOUR website! f(x) = 3x^3 + 9x^2 + 8x
f(x) = x(3x^2 + 9x + 8)
We know there is a root at zero for sure. Think about the quadratic part.
3x^2 + 9x + 8
Vertex: (-3/2,5/4) and the parabola opens upward, so no roots
Positive Roots: 0
Negative Roots: 0
Imaginery Roots: 0
There is only one root, and that root is at the origin.
The Descarte's Rule of Signs would tell you that you either have two negative roots and one imaginery root or three imaginery roots. We know that the ammount of imaginery roots must be an even number, so you would solve this way.
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