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November 08, 2025, 08:12:59 am
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Author Topic: Finding P(x)  (Read 1003 times)  Share 

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IndefatigableLover

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Finding P(x)
« on: March 20, 2013, 11:49:30 pm »
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This question has lost me completely because the book doesn't explain anything nor can I find anything on the Internet on how to determine an equation with only one solution.

"Given that P(x) is a cubic polynomial with coefficient of being 1, and -1 is a solution of the equation P(x) = 0, find P(x)"
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pi

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Re: Finding P(x)
« Reply #1 on: March 20, 2013, 11:57:51 pm »
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Think y=(x-a)^3 form?
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IndefatigableLover

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Re: Finding P(x)
« Reply #2 on: March 21, 2013, 12:06:14 am »
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Quote from: pi on March 20, 2013, 11:57:51 pm
Think y=(x-a)^3 form?
I've tried that but the answer in the book differs from it :/

Answer:
Spoiler
x^3-2x+3
« Last Edit: March 21, 2013, 12:13:57 am by IndefatigableLover »
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Professor Polonsky

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Re: Finding P(x)
« Reply #3 on: March 21, 2013, 12:10:00 am »
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That answer has got to be wrong. If the coefficient of x^3 is 1, it can't just disappear.
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IndefatigableLover

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Re: Finding P(x)
« Reply #4 on: March 21, 2013, 12:16:09 am »
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Quote from: Polonius on March 21, 2013, 12:10:00 am
That answer has got to be wrong. If the coefficient of x^3 is 1, it can't just disappear.
Sorry about that... I accidentally imputed the wrong answer in but yeah that answer is in the book although 'pi's' method does work too so there might be multiple solutions for this questions >.<

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Professor Polonsky

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Re: Finding P(x)
« Reply #5 on: March 21, 2013, 12:24:59 am »
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I'm pretty sure there are infinite solutions for this question, though I might be wrong. Though the answer you provided still doesn't seem to be one of them...

Basically any for which would be an answer.
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IndefatigableLover

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Re: Finding P(x)
« Reply #6 on: March 21, 2013, 12:30:12 am »
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Quote from: Polonius on March 21, 2013, 12:24:59 am
I'm pretty sure there are infinite solutions for this question, though I might be wrong. Though the answer you provided still doesn't seem to be one of them...

Basically any for which would be an answer.
Yeah I was trying to work from the answer and backtrack (although I shouldn't) but I couldn't figure out how they did it...
I might just leave it with a statement saying there are infinite solutions for the question or something like that but thanks for your help Polonius :)
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Professor Polonsky

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Re: Finding P(x)
« Reply #7 on: March 21, 2013, 12:39:30 am »
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Which textbook is the question from, by the way? In any case, I wouldn't worry about this too much. The best you can do is provide a correct solution.
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Mao

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Re: Finding P(x)
« Reply #8 on: March 21, 2013, 10:34:03 am »
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There are two classes of solutions:

for (note that it is possible for , and they can be negative)

for (note that can be negative)

So, any function that fits either of this form satisfies the original condition. There are infinite many solutions.
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