Yikes
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Ok folks - it has been a while. 10 years, to be exact. I'm helping my wife with some math homework. She's taking pre-calculus, and they're reviewing factoring, finding zeros, etc. However, I'm having trouble remembering how to find *all* real zeros, rational or irrational, of degree-3 or higher polynomials. She can't use a graphing calculator. What is the proper analytical way to find these? :confused: Thanks, math whizzes. :)
Jon Sagara
A bottle a night isn't alcoholism - it's persistence! -- A coworker, jokingly -
Ok folks - it has been a while. 10 years, to be exact. I'm helping my wife with some math homework. She's taking pre-calculus, and they're reviewing factoring, finding zeros, etc. However, I'm having trouble remembering how to find *all* real zeros, rational or irrational, of degree-3 or higher polynomials. She can't use a graphing calculator. What is the proper analytical way to find these? :confused: Thanks, math whizzes. :)
Jon Sagara
A bottle a night isn't alcoholism - it's persistence! -- A coworker, jokinglyShove all the terms on one side, set them equal to zero. Then factor the equation. Once you get it in factored form, you set each factor equal to zero and solve for x. Here's an example:
Original equation: x3 = 8x2 - 15x
x3 -8x2 + 15x = 0 //First we put all the terms on one side
x(x2 - 8x + 15) = 0 //Now we factor out one x to get it into binomial form
x(x-3)(x-5) = 0 //Now we factor the binomial (you just kinda have to "get it")First factor:
x = 0
Second factor:
x - 3 = 0
x = 3
Third factor:
x - 5 = 0
x = 5Thus:
x = 0, 3, 5Hope that helps. :)
Hawaian shirts and shorts work too in Summer. People assume you're either a complete nut (in which case not a worthy target) or so damn good you don't need to worry about camouflage... -Anna-Jayne Metcalfe on Paintballing
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Shove all the terms on one side, set them equal to zero. Then factor the equation. Once you get it in factored form, you set each factor equal to zero and solve for x. Here's an example:
Original equation: x3 = 8x2 - 15x
x3 -8x2 + 15x = 0 //First we put all the terms on one side
x(x2 - 8x + 15) = 0 //Now we factor out one x to get it into binomial form
x(x-3)(x-5) = 0 //Now we factor the binomial (you just kinda have to "get it")First factor:
x = 0
Second factor:
x - 3 = 0
x = 3
Third factor:
x - 5 = 0
x = 5Thus:
x = 0, 3, 5Hope that helps. :)
Hawaian shirts and shorts work too in Summer. People assume you're either a complete nut (in which case not a worthy target) or so damn good you don't need to worry about camouflage... -Anna-Jayne Metcalfe on Paintballing
Yes, she can do those. But how about a function with no rational zeros, such as
f(x) = 3x3- 9x + 1?Jon Sagara
A bottle a night isn't alcoholism - it's persistence! -- A coworker, jokingly -
Yes, she can do those. But how about a function with no rational zeros, such as
f(x) = 3x3- 9x + 1?Jon Sagara
A bottle a night isn't alcoholism - it's persistence! -- A coworker, jokinglyis this just an elaborate ruse to get me to help you with your homework? ;P Hmmm...let's see. I'm thinking you're going to have to do either polynomial long division or synthetic division... A quick google led to this excellent example: Page 1[^] Page 2[^]
Hawaian shirts and shorts work too in Summer. People assume you're either a complete nut (in which case not a worthy target) or so damn good you don't need to worry about camouflage... -Anna-Jayne Metcalfe on Paintballing
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is this just an elaborate ruse to get me to help you with your homework? ;P Hmmm...let's see. I'm thinking you're going to have to do either polynomial long division or synthetic division... A quick google led to this excellent example: Page 1[^] Page 2[^]
Hawaian shirts and shorts work too in Summer. People assume you're either a complete nut (in which case not a worthy target) or so damn good you don't need to worry about camouflage... -Anna-Jayne Metcalfe on Paintballing
David Stone wrote: is this just an elaborate ruse to get me to help you with your homework? Yes, my [EDIT] 1.5 2.5 :~ [/EDIT] years of higher math at Cal Poly just weren't enough. I had to go back to Pre-calc. ;P David Stone wrote: Hmmm...let's see. I'm thinking you're going to have to do either polynomial long division or synthetic division... A quick google led to this excellent example: Page 1[^] Page 2[^] Thanks for the links - I'll take a look. :)
Jon Sagara
A bottle a night isn't alcoholism - it's persistence! -- A coworker, jokingly -
David Stone wrote: is this just an elaborate ruse to get me to help you with your homework? Yes, my [EDIT] 1.5 2.5 :~ [/EDIT] years of higher math at Cal Poly just weren't enough. I had to go back to Pre-calc. ;P David Stone wrote: Hmmm...let's see. I'm thinking you're going to have to do either polynomial long division or synthetic division... A quick google led to this excellent example: Page 1[^] Page 2[^] Thanks for the links - I'll take a look. :)
Jon Sagara
A bottle a night isn't alcoholism - it's persistence! -- A coworker, jokinglyJon Sagara wrote: Yes, my [EDIT] 1.5 2.5 [/EDIT] years of higher math at Cal Poly just weren't enough. :laugh: Do I really need to say anything here? ;P :laugh:
Hawaian shirts and shorts work too in Summer. People assume you're either a complete nut (in which case not a worthy target) or so damn good you don't need to worry about camouflage... -Anna-Jayne Metcalfe on Paintballing
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Jon Sagara wrote: Yes, my [EDIT] 1.5 2.5 [/EDIT] years of higher math at Cal Poly just weren't enough. :laugh: Do I really need to say anything here? ;P :laugh:
Hawaian shirts and shorts work too in Summer. People assume you're either a complete nut (in which case not a worthy target) or so damn good you don't need to worry about camouflage... -Anna-Jayne Metcalfe on Paintballing
Nope. ;P
Jon Sagara
A bottle a night isn't alcoholism - it's persistence! -- A coworker, jokingly -
Yes, she can do those. But how about a function with no rational zeros, such as
f(x) = 3x3- 9x + 1?Jon Sagara
A bottle a night isn't alcoholism - it's persistence! -- A coworker, jokinglyUse Descartes' Rule of signs for the good start: Make use of Monomial factors, special products, rational roots, and of course synthetic division. Regardz Colin J Davies
*** WARNING *
This could be addictive
**The minion's version of "Catch :bob: "It's a real shame that people as stupid as you can work out how to use a computer. said by Christian Graus in the Soapbox
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Shove all the terms on one side, set them equal to zero. Then factor the equation. Once you get it in factored form, you set each factor equal to zero and solve for x. Here's an example:
Original equation: x3 = 8x2 - 15x
x3 -8x2 + 15x = 0 //First we put all the terms on one side
x(x2 - 8x + 15) = 0 //Now we factor out one x to get it into binomial form
x(x-3)(x-5) = 0 //Now we factor the binomial (you just kinda have to "get it")First factor:
x = 0
Second factor:
x - 3 = 0
x = 3
Third factor:
x - 5 = 0
x = 5Thus:
x = 0, 3, 5Hope that helps. :)
Hawaian shirts and shorts work too in Summer. People assume you're either a complete nut (in which case not a worthy target) or so damn good you don't need to worry about camouflage... -Anna-Jayne Metcalfe on Paintballing
You know what, it's been a very very long time since i see such mathematical equation. And it feels good as it brings back the memories that i had back in school then. :) Weiye, Chen When pursuing your dreams, don't forget to enjoy your life...
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Use Descartes' Rule of signs for the good start: Make use of Monomial factors, special products, rational roots, and of course synthetic division. Regardz Colin J Davies
*** WARNING *
This could be addictive
**The minion's version of "Catch :bob: "It's a real shame that people as stupid as you can work out how to use a computer. said by Christian Graus in the Soapbox
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LOL. :-) :beer: Regardz Colin J Davies
*** WARNING *
This could be addictive
**The minion's version of "Catch :bob: "It's a real shame that people as stupid as you can work out how to use a computer. said by Christian Graus in the Soapbox
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Ok folks - it has been a while. 10 years, to be exact. I'm helping my wife with some math homework. She's taking pre-calculus, and they're reviewing factoring, finding zeros, etc. However, I'm having trouble remembering how to find *all* real zeros, rational or irrational, of degree-3 or higher polynomials. She can't use a graphing calculator. What is the proper analytical way to find these? :confused: Thanks, math whizzes. :)
Jon Sagara
A bottle a night isn't alcoholism - it's persistence! -- A coworker, jokinglySeems like we have a good number of math whizes @ cp. I was good in high school maths but not much in engineering maths... Rakesh
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Shove all the terms on one side, set them equal to zero. Then factor the equation. Once you get it in factored form, you set each factor equal to zero and solve for x. Here's an example:
Original equation: x3 = 8x2 - 15x
x3 -8x2 + 15x = 0 //First we put all the terms on one side
x(x2 - 8x + 15) = 0 //Now we factor out one x to get it into binomial form
x(x-3)(x-5) = 0 //Now we factor the binomial (you just kinda have to "get it")First factor:
x = 0
Second factor:
x - 3 = 0
x = 3
Third factor:
x - 5 = 0
x = 5Thus:
x = 0, 3, 5Hope that helps. :)
Hawaian shirts and shorts work too in Summer. People assume you're either a complete nut (in which case not a worthy target) or so damn good you don't need to worry about camouflage... -Anna-Jayne Metcalfe on Paintballing
Cool, it's this kind of math I'm currently doing right NOW! :) Rickard Andersson Here is my card, contact me later! UIN: 50302279 Sonork: 37318 Interests: C++, ADO, SQL, Winsock, 0s and 1s
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is this just an elaborate ruse to get me to help you with your homework? ;P Hmmm...let's see. I'm thinking you're going to have to do either polynomial long division or synthetic division... A quick google led to this excellent example: Page 1[^] Page 2[^]
Hawaian shirts and shorts work too in Summer. People assume you're either a complete nut (in which case not a worthy target) or so damn good you don't need to worry about camouflage... -Anna-Jayne Metcalfe on Paintballing
David Stone wrote: Page 2[^] Here is Page 2! :) Rickard Andersson Here is my card, contact me later! UIN: 50302279 Sonork: 37318 Interests: C++, ADO, SQL, Winsock, 0s and 1s
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Ok folks - it has been a while. 10 years, to be exact. I'm helping my wife with some math homework. She's taking pre-calculus, and they're reviewing factoring, finding zeros, etc. However, I'm having trouble remembering how to find *all* real zeros, rational or irrational, of degree-3 or higher polynomials. She can't use a graphing calculator. What is the proper analytical way to find these? :confused: Thanks, math whizzes. :)
Jon Sagara
A bottle a night isn't alcoholism - it's persistence! -- A coworker, jokinglyCurses! You forced me to look back through my textbooks; after 23 years of working in the real world and needing none of it, I'm amazed at how much I used to know! There were numerous methods and shortcuts presented in class, all in engineering classes rather than in math, but I don't recall them. I do remember solving these by long division before the first programmable calculators were introduced, and it was extremely tedious. Perversely, though, I enjoyed it immensely. It was a lot of trial and error, and as I recall, it is best to start with quadratic roots first, then linear roots, then recheck for repeated roots. Complex roots are found by applying the formula for the solution of quadratic equations, if any exist. Drat... now you've got me wanting to go back through the books and relearn all that fun stuff. But where to start? Linear Control Systems: Design and Analysis, Elementary Differential Equations, Active Filter Design and Synthesis, Tensor Analysis, Div, Grad, Curl, And All That... :sigh: "Some people are like Slinkies... not really good for anything,
but you still can't help but smile when you see one
tumble down the stairs." -
Ok folks - it has been a while. 10 years, to be exact. I'm helping my wife with some math homework. She's taking pre-calculus, and they're reviewing factoring, finding zeros, etc. However, I'm having trouble remembering how to find *all* real zeros, rational or irrational, of degree-3 or higher polynomials. She can't use a graphing calculator. What is the proper analytical way to find these? :confused: Thanks, math whizzes. :)
Jon Sagara
A bottle a night isn't alcoholism - it's persistence! -- A coworker, jokinglyFor you Revenge of the Nerds fans... <"Ogre" voice>Nerds!</"Ogre" voice> For those of you who don't know who I'm talking about, go rent the movie..."Ogre" is the big ugly bearded guy ;) Jeremy Kimball
