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Find Descartes rule x^3+3x^2+3x+1 [ Calculator, Method and examples ]

Your problem `->` Descartes rule x^3+3x^2+3x+1

Here `f(x)=x^3+3x^2+3x+1`


look first at `f(x)`: (positive case)

Sign change count`color{blue}{+}` to `color{blue}{+}`
`color{blue}{+}` to `color{blue}{+}`
`color{blue}{+}` to `color{blue}{+}`

There are no sign changes, so there are no positive roots.

Now look at `f(–x)`: (negative case)



Sign change count`color{red}{-}` to `color{blue}{+}`
`color{blue}{+}` to `color{red}{-}`
`color{red}{-}` to `color{blue}{+}`

There are 3 sign changes, so there are 3 or counting down in pairs, 1 negative roots.

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