Descartes himself used the transformation for using his rule for getting information of the number of negative roots.

Descartes’ Rule of Signs - How hard can it be? Descartes' Rule of Signs will not tell me where the polynomial's zeroes are (I'll need to use the Rational Roots Test and synthetic division, or draw a graph, to actually find the roots), but the Rule will tell me how many roots I can expect, and of which type. Historical Note: The Rule of Signs was first described by René Descartes in 1637, and is sometimes called Descartes' Rule of Signs. Descartes rule of signs and homographic transformations of the variable are, nowadays, the basis of the fastest algorithms for computer computation of real roots of polynomials (see Real-root isolation). 1) f (x) = 3x4 + 20 x2 − 32 Possible # positive real zeros: 1 Possible # negative real zeros: 1 2) f (x) = 5x4 − 42 x2 + 49 Possible # positive real zeros: 2 or 0 Possible # negative … In order to find the number of negative zeros we find f(-x) and count the number of changes in sign for the coefficients: The move was reverted by David Eppstein twice. Descartes' rule of signs is a criterion which gives an upper bound on the number of positive or negative real roots of a polynomial with real coefficients. The rule is actually simple. 1) f (x) = 3x4 + 20 x2 − 32 Possible # positive real zeros: 1 Possible # negative real zeros: 1 … Descartes' rule of signs – The rule is to use "s's" per WP:MOS as Cherkash seems to insist. Descartes´ rule of signs tells us that the we then have exactly 3 real positive zeros or less but an odd number of zeros. We are interested in two kinds of real roots, namely positive and negative real roots. In mathematics, Descartes' rule of signs, first described by René Descartes in his work La Géométrie, is a technique for determining the number of positive or negative real roots of a polynomial. There is a straightforward way to determine the possible numbers of positive and negative real zeros for any polynomial function. 2 EXAMPLE 1 Use Descartes’ Rule of Signs to determine the number of possible positive and negative real solutions of the equation P(x) = 2x7 +15x6 +31x5 −x4 −49x3 −52x2 −78x−36 = 0. The purpose of the Descartes’ Rule of Signs is to provide an insight on how many real roots a polynomial P\left( x \right) may have. Algebra Index. In mathematics, Descartes' rule of signs, first described by René Descartes in his work La Géométrie, is a technique for determining an upper bound on the number of positive or negative real roots of a polynomial. Descartes’ Rule of Signs. Descartes’ Rule of Signs; Descartes’ Rule of Signs can be used to determine the number of positive real zeros, negative real zeros, and imaginary zeros in a polynomial function.