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March 30, 2017

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if the domain is the set of integers, the solution set of x^2 -3x -4<0 is what?

  • math - ,

    What your question really asks for is,
    "For what values of x does the corresponding parabola
    y = x^2 - 3x - 4 fall below the x-axis?"

    let's find the x-intercepts ....
    x^2 - 3x - 4 = 0
    (x-4)(x+1) = 0
    x = -1 or x = 4

    so the expression is < 0 for -1 < x < 4

    or

    (x+1)(x-4) < 0
    ( x+1 >0 AND x-4<0) OR ( x+1 < 0 AND x-4>0)
    ( x>-1 and x<4) OR (x<-1 AND x > 4)
    x>-1 and x<4 OR (null set)

    -1 < x < 4

  • math - ,

    thank you, so anything between -1 and 4 would be my answer? (0,1,2,3)?

  • math - ,

    yes.

  • math - ,

    Since your domain is integers, only the integers (0,1,2,3) satisfy the inequality. Otherwise, there would be an infinite number of non-integer solutions between -1 and 4.

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