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Quadratic Equations

  1. Apr 1, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the number of integral values of 'k' for which the quadratic equation 2x^2 +kx - 4=0 will have two rational solutions.

    2. Relevant equations

    d=(b^2- 4ac)^(1/2)

    3. The attempt at a solution

    If discriminant is a perfect square, then the roots will be rational and unequal. but for how many values of 'k' starting from 2 itself will I check th discriminant to be a perfect square????
  2. jcsd
  3. Apr 1, 2008 #2


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    The discriminant is k^2+32. So k^2+32=n^2 where n is an integer. n^2-k^2=32. But n^2-k^2=(n-k)*(n+k). How high do you need to check?
  4. Apr 1, 2008 #3
    n is at least k+1, so n^2-k^2 >= (k+1)^2 - k^2 = 2k + 1
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