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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 (x3) and (x1)^2 respectively.then,what is the remainder when it is divided by (x3){(x1)^2} 2. find all polynomials P satisfying p(x+1)=p(x)+2x+1 3. if all the roots of the polynomial equation x^44x^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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