Variation in Sign of Polynomial/Examples/Arbitrary Example 1
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Examples of Variations in Sign of Polynomial
Consider the polynomial equation over real numbers:
- $x^5 + x^4 - 2 x^3 + x^2 - 1 = 0$
This has three variations in sign:
- from $x^4$ to $-2 x^3$, where it goes from positive to negative
- from $-2 x^3$ to $x^2$, where it goes from negative to positive
- from $x^2$ to $-1$, where it goes from positive to negative.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Descartes's rule of signs
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Descartes's rule of signs