BUILT-IN MATHEMATICA SYMBOL

# RootIntervals

RootIntervals[{poly1, poly2, ...}]
gives a list of isolating intervals for the real roots of any of the , together with a list of which polynomials actually have each successive root.

RootIntervals[poly]
gives isolating intervals for real roots of a single polynomial.

RootIntervals[polys, Complexes]
gives bounding rectangles for complex roots.

## DetailsDetails

• The coefficients of poly must be integers or rationals.
• An isolating interval for a root of a polynomial poly is an interval where the only root of poly contained in the interval is .
• If a root is real, the isolating interval is an open real interval, or a point. If a root is not real, the isolating interval is an open rectangle, disjoint from the real axis.
• Multiple roots give multiple entries in the second list generated by RootIntervals.

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Get isolating intervals, together with a list of which polynomial has which root:

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The isolating intervals are always specified by exact rationals:

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