Polynomial

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Albi

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The polynomial [MATH] p(x) = x^{3} + ax^{2} + bx + c[/MATH] is given. Determine the parameters a,b and c, so that this polynomial is divisible by x-1
 
p(x) divisible by (x-1) [MATH]\implies[/MATH] p(1) = 0

what now?
 
Albi said:
The polynomial [MATH] p(x) = x^{3} + ax^{2} + bx + c[/MATH] is given. Determine the parameters a,b and c, so that this polynomial is divisible by x-1
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I'm not sure what this means. If the polynomial is given, then that means you know a, b, and c, and there is nothing to do. If it doesn't mean that, then there are infinitely many answers, so it's unclear in what form an answer should be given. You can, I suppose, write one equation that a, b, and c must satisfy; have you tried that?

Please state the exact wording of the problem as given to you, including any context that indicates how to answer. What topic are you studying?
 
Determine the parameters a,b and c, so that this polynomial is divisible by x-1.

This problem does not have an answer.
 
Albi said:
Okay, my mistake I didn't pose the question the right way
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The important thing is not how you posed it, but how it was posed to you!

Jomo, I think, is assuming one possible meaning, that you are to find one such polynomial. But that is too easy. I'm guessing that you are to characterize all such polynomials, which can be done with an equation suggested in post #2.

I want to be sure what someone is asking you to do. Is this an assignment from a course, or something else?
 
Dr.Peterson said:
The important thing is not how you posed it, but how it was posed to you!

Jomo, I think, is assuming one possible meaning, that you are to find one such polynomial. But that is too easy. I'm guessing that you are to characterize all such polynomials, which can be done with an equation suggested in post #2.

I want to be sure what someone is asking you to do. Is this an assignment from a course, or something else?
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Yes it is a question from course, but the question on the textbook is not in English
 
Albi said:
Yes it is a question from course, but the question on the textbook is not in English
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In that case (which is very common) I ask for both the exact original, which sometimes gives useful information just in the way it is arranged (if you give us an image), or in specific words we can look up, and also a translation as close as you can get. In this case, the important details may be subtleties in the grammar that we couldn't see, so perhaps it wouldn't help.
 
The answer was given in skeeter's first reply- if a polynomial, p(x), is divisible by x- r then p(r)= 0. Here the polynomial is p(x)= x3+ ax2+ bx+ c and r= 1 so we must have 1+ a+ b+ c= 0. Any values of a, b, and c such that 1+ a+ b+ c= 0 will make that true. For example, choosing a= 1 and b= c= -1 we have p(x)= x3+ x2- x- 1= (x- 1)(x2+ 2x+ 1). Or if b= 1 and a= c= -1 we have p(x)= x3- x2+ x- 1= (x- 1)(x^2+ 1), etc. There are infinitely many solutions.
 
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