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martindcx1e
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10-19-2007, 07:06 AM
Post subject: Another calc prob if you don't mind
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#1 (permalink)
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4-of-a-Kind
Join Date: Mar 2005
Posts: 3,614
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Alright here's one more for yall. I don't even know where to start on this kind of problem. Help plz?
Show that the equation x^101 + x^51 + x - 1 = 0 has exactly one real root.
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Wikipedia is the best thing ever. Anyone in the world can write anything they want about any subject. So you know you are getting the best possible information.
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mcatdog
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4-of-a-Kind
Join Date: Oct 2005
Location: St. Louis
Posts: 3,654
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hint #1: graph its derivative
hint #2: evaluate f(0) and f(1)
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martindcx1e
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4-of-a-Kind
Join Date: Mar 2005
Posts: 3,614
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what if i'm supposed to do it without graphing? also, i'd like the most general method of showing this so i can do it for different equations too.
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Wikipedia is the best thing ever. Anyone in the world can write anything they want about any subject. So you know you are getting the best possible information.
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mcatdog
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4-of-a-Kind
Join Date: Oct 2005
Location: St. Louis
Posts: 3,654
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I'm trying to let you figure it out without giving it away
just take the derivative and see if you can figure out any properties that it might have, if not then try to graph it
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spoonitnow
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Straight Flush
Join Date: Sep 2005
Location: IRC Chat Room
Posts: 5,406
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OP, You're seriously overthinking this imo.
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Quote:
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Originally Posted by Ripptyde
I only have 2 simple rules when I am coaching a new student.
Rule # 1: don't ask questions
Rule # 2: don't ask questions
I have no interest in discussing strategy with a protege'. Your job is to remain quiet and listen. I have a very systematic approach that I will share with the right candidate and I promise that I will turn you into a force of nature and show you elements of the game of poker that you never knew existed.
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Miffed22001
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Straight Flush
Join Date: Jun 2005
Location: Marry Me Cheryl!!!
Posts: 8,181
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ill be damned if i know the answer 
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gabe
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Moderator
Join Date: Dec 2004
Location: trying to live
Posts: 7,964
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Quote:
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Originally Posted by mcatdog
I'm trying to let you figure it out without giving it away
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lame!!!
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spoonitnow
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Straight Flush
Join Date: Sep 2005
Location: IRC Chat Room
Posts: 5,406
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This is how bored I am.
Let f(x) = x^101 + x^51 + x − 1.
First we prove existence of some number of roots: Since the limit as x approaches -infinity is -infinity and the limit as x approaches infinity is infinity, there has to be at least one root on (-infinity, infinity).
Now we narrow it down: When we take the derivative, we get f'(x) = 101x^100 + 51x^50 + 1. We note that f'(x) > 0 for all x (all powers are even, all coefficients are positive, and the constant term is positive). Now if there was more than one root, then by Rolle's Theorem, there would be a c such that f'(c) = 0. However, f'(c) is always positive, so there is only one root.
Hit me back in this thread or a PM if you don't get it. Applied Math major ftw.
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Quote:
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Originally Posted by Ripptyde
I only have 2 simple rules when I am coaching a new student.
Rule # 1: don't ask questions
Rule # 2: don't ask questions
I have no interest in discussing strategy with a protege'. Your job is to remain quiet and listen. I have a very systematic approach that I will share with the right candidate and I promise that I will turn you into a force of nature and show you elements of the game of poker that you never knew existed.
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Miffed22001
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Straight Flush
Join Date: Jun 2005
Location: Marry Me Cheryl!!!
Posts: 8,181
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im still stuggling with E=mc2 ffs.
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