The number of real roots of an algebraic equation with real coefficients whose real roots are simple over an interval, the endpoints of which are not roots, is equal to the difference between the number of sign changes of the Sturm chains formed for the interval ends.

# Sturm Theorem

## See also

Sturm Chain, Sturm Function## Explore with Wolfram|Alpha

## References

Dörrie, H. "Sturm's Problem of the Number of Roots." §24 in*100 Great Problems of Elementary Mathematics: Their History and Solutions.*New York: Dover, pp. 112-116, 1965.Rusin, D. "Known Math." http://www.math.niu.edu/~rusin/known-math/96/sturm.

## Referenced on Wolfram|Alpha

Sturm Theorem## Cite this as:

Weisstein, Eric W. "Sturm Theorem." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/SturmTheorem.html