Recent content by daveclifford

can someone help, please? :cry:

http://onlinemathcircle.com/wp-content/uploads/2011/07/Lecture_Polynomials.pdf (pg 4) the whole text is in this website http://mathweb.scranton.edu/monks/courses/ProblemSolving/POLYTHEOREMS.pdf (pg 7, No. 10) another similar text

(Lower Bound)(Let P(x) be any polynomial with real coefficients and a positive leading coefficient.) Let r be a root of the given polynomial. Assuming r is not equal to 0 and that the polynomial has a nonzero constant term. Since P(r)=0, we can say that P(x)=(x-r)Q(x). Substituting in x=a, we...

Recently I am studying about theorems regarding to polynomial equations and encounter the lower and upper bounds theorem. Which states that if a<0 and P(a) not equals 0, and dividing P(x) by (x-a) leads to coefficients that alternate signs, then a is a lower bound of all the roots of P(x)=0. The...