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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)� + 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. Tags polynomials Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post tahir.iman Algebra 1 January 27th, 2013 08:56 PM ElMarsh Linear Algebra 3 October 15th, 2009 04:14 PM lime Abstract Algebra 0 February 19th, 2009 12:19 AM SAT_frinzzy New Users 0 September 1st, 2008 07:08 AM missunique Algebra 4 March 24th, 2008 05:04 PM

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