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 Algebra Pre-Algebra and Basic Algebra Math Forum

 April 8th, 2014, 02:49 AM #1 Senior Member   Joined: Oct 2013 From: Far far away Posts: 431 Thanks: 18 quadratic function Prove that there is a quadratic function f(n) = n^2 + bn + c with positive integer coefficients b, c such that f(n) is composite (i.e. not prime) for all positive integers n, or else prove that the statement is false. I don't even know where to start so any help will be deeply appreciated. thanks April 8th, 2014, 03:58 AM #2 Math Team   Joined: Apr 2010 Posts: 2,780 Thanks: 361 A quadratic function is composite if you can factor it in at least two polynomials each different from one with integer coefficients. To prove that there is a quadratic function f(n) = n^2 + bn + c with positive integer coefficients b, c such that f(n) is composite (i.e. not prime) for all positive integers n, you just need to find an example. A general quadratic function (with respect to n) is an^2 + bn + c But in your case, a = 1 so you cannot factor out a constant. Another lower degree polynomial is of the form wn + x, of which there are two factors. Can you find two polynomials of the form wn + x such that when multiplied you get such a function? Thanks from shunya Tags function, quadratic 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 jiasyuen Calculus 2 October 7th, 2013 06:30 AM Ccamm Algebra 5 May 6th, 2013 04:49 PM Sarii Applied Math 0 April 23rd, 2013 07:33 AM lalex0710 Algebra 9 October 16th, 2012 08:39 AM killcam Algebra 1 July 6th, 2012 09:14 PM

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