Math Goodies is a free math help portal for students, teachers, and parents.
|
Interactive Math Goodies Software

testing left nav
Math Forums @ Math Goodies
Home | Profile | Active Topics | Members | Search | FAQ
 All Forums  Homework Help Forums  Pre-Calculus and Calculus  Lower bound of polynomial zeros New Topic  Reply to Topic  Printer Friendly
Author  Topic

moon1130
Senior Member

USA
24 Posts

 Posted - 08/10/2013 :  14:47:48 Hi,I have the polynomial function F(x)= x+11x+31x+21, which factors to (x+1)*(x+3)*(x+7). From the factorization, it is clear that x=-8 is a lower bound of the real zeros. Yet, when I divide the function by -8 using synthetic division, the last row of the synthetic division is 1 3 7 -35 rather than 1 -3 7 -35, which it should be if -8 were a lower bound according to the Upper and Lower Bounds Theorem. I have checked my division several times and I come up with the same result. Why is the lower bound theorem failing here?Thank you for any help you can give me.

Ultraglide

299 Posts

 Posted - 08/12/2013 :  22:03:46 This being a cubic function, it has no bounds, horizonally or vertically.

royhaas
Moderator

USA
3059 Posts

 Posted - 08/13/2013 :  08:03:41 The section "Polynomials with real roots" in http://en.wikipedia.org/wiki/Properties_of_polynomial_rootsshould give some help.

Ultraglide

299 Posts

 Posted - 08/13/2013 :  09:45:23 Just a note: since you have factored the polynomial (I curious as to how the word 'factorize' has crept into use in some areas), you will note that it the zeros occur at -1, -3, and -7 but not at -8. Maybe you need to try using one of the first three numbers in your synthetic division.

moon1130
Senior Member

USA
24 Posts

 Posted - 09/10/2013 :  17:23:58 Thank you Ultraglide and Royhaas for your responses.According to my text, the lower bound of a polynomial function is any number to the left of the smallest negative zero. Since -7 is the smallest negative zero, -8, -9, etc. are each lower bounds for this function. This being the case, when I divide the polynomial by -8 using synthetic division, one would expect that the quotient would have the alternating sign form of + - + - or - + = +.....rather than + + + -. I could not figure out why this non-alternating form.Thanks for your help,moon1130
Topic
 New Topic  Reply to Topic  Printer Friendly Jump To: Select Forum New Visitor Forum       Testing Forum Homework Help Forums       Basic Math and Pre-Algebra       Algebra       Geometry and Trigonometry       Pre-Calculus and Calculus       Probability and Statistics       Standardized Test Preparation Help       Miscellaneous Math Topics Educator Forum       Teacher Talk Parent Forum       Parent's Place  -------------------- Home Active Topics Frequently Asked Questions Member Information Search Page
 Math Forums @ Math Goodies © 2000-2004 Snitz Communications