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Quadratic equations

  1. Oct 28, 2014 #1
    1. The problem statement, all variables and given/known data
    If roots of the equation x^2 - (2n+18)x - n - 11 = 0 (n is an integer) are rational for n=a and n=b then |a-b| is
    Ans: 3

    2. Relevant equations

    3. The attempt at a solution
    On substituting a (or b) into the quadratic, the roots are rational.
    If the roots are rational, then the discriminant must be a perfect square (and positive).
    Hence, (2a+18)^2 + 4(a+11) = k^2
    On simplifying,
    a^2 + 19a + 92 = k^2 and a^2 + 19a + 92 > 0

    What do I do after this?
  2. jcsd
  3. Oct 29, 2014 #2


    Staff: Mentor

    Can you subtract the b version from the a version, simplify and then see if you can get the absolute value answer?

    Perhaps the absolute value trick of using the square root will help?

    abs(x) = sqrt(x^2)
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