Variation in Sign of Polynomial/Examples

Examples of Variations in Sign of Polynomial

Arbitrary Example

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.