Pre Calc

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Solve the non-linear inequality:

x^3-5x^2-14x<0

  • Pre Calc -

    x^3-5x^2-14x<0

    x(x^2 - 5x - 14) < 0
    x(x-7)(x+2) < 0

    so we have 3 critical values:
    x = 0, -2, and 7

    investigate each domain

    1. x < -2 , I will pick x = -5
    (-)(-)(-) which is < 0 , that works
    2. between -2 and 0, I will pick x = -1
    (-)(-1)(+) > 0 , no good
    3. between 0 and 7, I will pick x = 1
    (+)(-)(+) < 0 , yup, that works
    4. x > 7, I will pick x = 10
    (+)(+)(+) > 0 , no good

    so x < -2 OR 0 < x < 7

    notice I did not actually have to find the algebraic answer, just determine if the result is + or -

  • Pre Calc -

    thanks!

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