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Math Help - equation

  1. #1
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    equation

    Y=X+12X+36X is used to find solutions of the equation X+12X+36X=k for various values

    The maximum point is (-6,0)
    The minimum point is (-2,-32)
    1) Verify the point (-8,-32) is on the graph
    2) Find the number of real roots of the equation when k is:
    i) 0
    ii) 20
    iii) -20
    iv) -40
    3) For what value of k does the equation have three real roots? What can you say about these roots?
    any help would be fab
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  2. #2
    GAMMA Mathematics
    colby2152's Avatar
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    I do not understand your question. Using your given polynomial, the point (-8, -32) is not a valid coordinate of the graph.
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  3. #3
    Senior Member JaneBennet's Avatar
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    (−8,−32) is on the graph y = x^3+12x^2+36x.

    So, the y-value of the local maximum is 0 and the y-value of the local minimum is is −32. What this means is that for −32 ≤ k ≤ 0, the equation x^3+12x^2+36x=k has three real roots. (In the case k = −32 or 0, two of the real roots are repeated.) For k < −32 or k > 0, the equation x^3+12x^2+36x=k has only one real root.
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