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September 4th, 2010, 07:09 AM   #1
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3 polynomials.......

1. a polynomial f(x) leaves remainder 15 and (2x+1) when divided by (x-3) and (x-1)^2 respectively.then,what is the remainder when it is divided by (x-3){(x-1)^2}

2. find all polynomials P satisfying p(x+1)=p(x)+2x+1

3. if all the roots of the polynomial equation
x^4-4x^3+ax^2+bx+1=0 are positive real numbers,show that all the roots are equal.

please help!
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September 4th, 2010, 07:10 AM   #2
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Re: 3 polynomials.......

I have observed that p(x)=x^2 satisfies the given condition. Do we now have to substitute p(x) in the condition?
How should we substitute?
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September 4th, 2010, 01:03 PM   #3
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Re: 3 polynomials.......

DEL
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September 4th, 2010, 01:13 PM   #4
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1. Hint: you're looking for a function that can be written as a(x - 1) + 2x + 1 and has the value 15 when x = 3.

2. Let P(x) ? x + Q(x), so that Q(x+1) ? Q(x). It follows (do you see why?) that Q(x) is a constant.
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