Alegra

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solve the inequality express in interval notation
x^4 + 4x^3 - 9x^2 - 36x < 0

  • Algebra -

    Assistance needed.

  • Alegra -

    Ah yeah which is why I post the question.

  • Alegra -

    Alissa -- Writeacher corrected your spelling of "Algebra" so that a math expert would see your post.

    Jiskha doesn't have any experts in Alegra (whatever that is).

  • Alegra -

    x^4 + 4x^3 - 9x^2 - 36x
    = x(x^3 + 4x^2 - 9x - 36)

    Cubics are hard to solve, so look for easy roots. They will be factors of 36.

    A little synthetic division reveals

    (x+4)(x+3)x(x-3)

    Now since everything is single roots, the graph alternates between positive and negative between roots.

    Since it's a quartic with a positive coefficient, it will be positive before the lowest root and after the highest root.

    So,

    y > 0 for x < -4
    y < 0 for -4 < x < -3
    y > 0 for -3 < x < 0
    y < 0 for 0 < x < 3
    y > 0 for x > 3

  • Alegra -

    Thank you I appreciate your help and the fact that you didn't make a big issue out of a typo. Again thank you.

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