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 September 4th, 2010, 07:09 AM #1 Newbie   Joined: Jun 2009 Posts: 14 Thanks: 0 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!
 September 4th, 2010, 07:10 AM #2 Newbie   Joined: Jun 2009 Posts: 14 Thanks: 0 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?
 September 4th, 2010, 01:03 PM #3 Newbie   Joined: Aug 2010 Posts: 25 Thanks: 0 Re: 3 polynomials....... DEL
 September 4th, 2010, 01:13 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,926 Thanks: 2205 1.  Hint: you're looking for a function that can be written as a(x - 1)² + 2x + 1 and has the value 15 when x = 3. 2.  Let P(x) ? x² + 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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