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algebra

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

  • algebra -

    x(x^3 + 4x^2 - 9x - 36) < 0
    x( x^2(x+4) - 9(x+4) ) = 0
    x(x+4)(x^2-9) < 0
    x(x+4)(x+3)(x-3) < 0

    so your critical values are
    x = 0, -3, -4, and 3

    Knowing that y = x^4 + .... is a quartic that rises in the 1st and 2nd quadrant because of the +1x^4 term, and it has 4 x-intercepts, you can make a rough sketch showing a W shape with those intercepts.

    It should be obvious that the graph is below the x-axis ( y < 0 ) for values between -3 and -4 or between 0 and 3
    so in standard notation:
    -4 < x < -3 OR 0 < x < 3

    I will leave it up to you to express it in interval notation

  • algebra -

    Thank you!

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