Analytically solve the following inequality?

x^6+12x-20x^2-5x^3<8x^5-18x^4

construct a sign diagram to support the answer.

Thank you!

3 Answers

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  • Ian H
    Lv 7
    4 weeks ago

    x^6 - 8x^5 + 18x^4 - 5x^3 - 20x^2 + 12x < 0

    This graph illustrates the intervals when f(x) < 0

    https://www.wolframalpha.com/input/?i=x%5E6+-+8x%5...

    (x – 1)x(x + 2)^2* (x^2 – 5x + 3) = 0 gives the roots in detail as

    -1, 0, 2, [5 -√(3)]/2, [5 +√(3)]/2 

    You can now construct your sign diagram 

  • 4 weeks ago

    x^6 + 12x - 20x^2 - 5x^3 < 8x^5 - 18x^4

    x^6 - 8x^5 + 18x^4 + 12x - 20x^2 - 5x^3 < 0

    (x - 2)^2 x (x + 1) (x^2 - 5 x + 3) < 0

    Integer solutions:

    x = 1

    x = 3

    x = 4

  • david
    Lv 7
    4 weeks ago

    x^6+12x-20x^2-5x^3<8x^5-18x^4

    x(x + 2)(x^4 - 2x^3 + 4x^2 - 13x + 6) < 2x^4(4x - 9)

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