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Math Help - Algebra + Polynomials

  1. #1
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    Algebra + Polynomials

    The polynomial 13 x^2+ kx+35 is to be factored into two linear prime binomials with integer coefficients. This can be done if k is:
    a)any even number
    b) some even number
    c) any odd number
    d) some odd number
    e) zero

    Im thinking its either c or d but im not sure which?
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  2. #2
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    for the solutions to be integers firstly consider

    and therefore make sure you are finding real numbers first, integers are a subset of real numbers. In your case a = 13, b=k & c=35

     b^2-4ac >0

     k^2-4(13)(35) >0

     k^2-1820 >0

     k^2>1820

     k>\sqrt{1820} \approx 42

    Now we know what to expect for k.

    As 13 is a prime number you can expect your solution to look like

    (13x+A)(x+B) where A\times B = 35. Try factors of 35 for A & B and expand this equation to find the middle term to be >42.
    Last edited by pickslides; May 24th 2009 at 03:29 PM. Reason: Typo
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