scholarly journals A Few Riddles Behind Rolle’s Theorem

2012 ◽  
Vol 119 (9) ◽  
pp. 787 ◽  
Author(s):  
B. Shapiro ◽  
M. Shapiro
Keyword(s):  
Rolle’S Theorem

On Rolle's Theorem

1979 ◽  
Vol 86 (6) ◽  
pp. 486 ◽  
Author(s):  
Hans Samelson
Keyword(s):  
Rolle’S Theorem

scholarly journals Ordered fields satisfying Rolle's theorem

1986 ◽  
Vol 30 (1) ◽  
pp. 66-78 ◽  
Author(s):  
Ron Brown ◽  
Thomas C. Craven ◽  
M.J. Pelling
Keyword(s):  
Rolle’S Theorem ◽  
Ordered Fields

A Complex Rolle's Theorem

1992 ◽  
Vol 99 (9) ◽  
pp. 858-861 ◽  
Author(s):  
J.-Cl. Evard ◽  
F. Jafari
Keyword(s):  
Rolle’S Theorem

Counting zeros of generalised polynomials: Descartes’ rule of signs and Laguerre’s extensions

2006 ◽  
Vol 90 (518) ◽  
pp. 223-234 ◽  
Author(s):  
G. J. O. Jameson
Keyword(s):  
Basic Result ◽  
Real Polynomial ◽  
Real Zeros ◽  
Analytic Proof ◽  
Sign Changes ◽  
Rolle’S Theorem

One of the bedrock theorems of mathematics is the statement that a real polynomial of degree n has at most n real zeros. Probably the best-known proof is the algebraic one, by factorisation. But there is also a pleasant analytic proof, by deduction from Rolle’s theorem. A slightly different question is how many positive zeros a polynomial has. Here the basic result is known as ‘Descartes′ rule of signs’. It says that the number of positive zeros is no more than the number of sign changes in the sequence of coefficients. Descartes included it in his treatise La Géométrie which appeared in 1637. It can be proved by a method based on factorisation, but, again, just as easily by deduction from Rolle’s theorem.

An Ultimate Proof of Rolle's Theorem

1979 ◽  
Vol 86 (6) ◽  
pp. 484 ◽  
Author(s):  
Alexander Abian
Keyword(s):  
Rolle’S Theorem
Sign in / Sign up

Export Citation Format

Share Document