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- Mar 5th 2012, 06:15 AM #1

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## please help!! x^3 + ax^2 + bx+ c

Hi

so I am a student of Maths and Physics Track in my school

And in todays class in Maths, the teacher gave us a question. And when no one could solve it, he said that there is going to be a quiz in it tomorrow

I tried to solve it several times but I couldn't solve it

anyways,, the question is

if :: x^3 + ax^2 + bx + c

the rest of dividing it on (x-1) is :: 4

the rest of dividing it on (x+1) is :: -1

find :: a , b , c

- Mar 5th 2012, 06:22 AM #2

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- Mar 5th 2012, 09:46 AM #3

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## Re: please help!! x^3 + ax^2 + bx+ c

The remainder when polynomial f(x) is divided by x-a is f(a). Considering this you get a+b+c = 3 abd a-b+c = 0. So b = 3/2 and a+c = 3/2. You can only have the solution in that form unless you have more information about the concerned polynomial.

- Mar 5th 2012, 11:47 AM #4

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- Mar 5th 2012, 11:54 AM #5

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- Mar 5th 2012, 11:57 AM #6

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- Mar 5th 2012, 12:11 PM #7

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## Re: please help!! x^3 + ax^2 + bx+ c

The remark of the remainder of f(x) being f(a) when divided by x-a is the statement of the remainder theorem, and the letter

*a*is not the coefficient*a*of your problem here. The 3 appeared because f(1) = 4 implies 1+a+b+c = 4 which implies a+b+c = 3.

- Mar 5th 2012, 12:28 PM #8

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- Mar 5th 2012, 12:45 PM #9

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- Mar 5th 2012, 12:56 PM #10

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- Mar 5th 2012, 01:46 PM #11

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- Mar 5th 2012, 02:12 PM #12

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## Re: please help!! x^3 + ax^2 + bx+ c

I'm glad I was of help.

Yes, you subtract the two equations from one another:

a+b+c = 3

a-b+c = 0

----------

2b = 3

=> b = 3/2.

a = -2.5

b = 1.5

c = 4

I would leave it in the general form unless the teacher asked only for a pair or you have more restrictions on the given polynomial.