solve using an interval sign table?

a) 2(x+3)(x-1)(x-5)<=0

b) -3(x+4)(x-3)^3>0

2 Answers

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  • 4 weeks ago
    Favourite answer

    a) x = -3, 1 and 5 are values that give zero

    so, for x < -3, say -4 we get:

    2(-4 + 3)(-4 - 1)(-4 - 5) = 2(-1)(-5)(-9) < 0

    For -3 < x < 1, say 0 we get:

    2(0 + 3)(0 - 1)(0 - 5) = 2(3)(-1)(-5) > 0

    For 1 < x < 5, say 2 we have:

    2(2 + 3)(2 - 1)(2 - 5) = 2(5)(1)(-3) < 0

    And for x > 5, say 6 we have:

    2(6 + 3)(6 - 1)(6 - 5) = 2(9)(5)(1) > 0

    so, for x < -3 or when 1 < x < 5 we have < 0

    Hence, for x ≤ -3 or when 1 ≤ x ≤ 5 we have  ≤ 0

    i.e. (-∞, -3] ∪ [1, 5]....using interval notation

    :)> 

  • rotchm
    Lv 7
    4 weeks ago

    Strange that you would ask for help for such elementary questions when in the past you have been doing much more advanced math than that!

    Are you at least trying? Take your time to read the question and to understand what they want. Depending on the sighs of a, b & c, when is a*b*c positive? That is what they are basically asking. 

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