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Math Help - Polynomials and Solving Inequalities...

  1. #1
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    Exclamation Polynomials and Solving Inequalities...

    I need help getting the answers for these 2 questions!
    I want to see if i did them right... (because i dont have an answer sheet)



    1) Solve 12x^3 - 16x^2 + 7x -1
    Let f(x) = 12x^3 - 16x^2 + 7x -1


    2) Solve the inequality:
    3x / (x^2 -4) < -1

    *note: where the "<" is, its supposed to be less than/equal to. (i just cant find a key for it :P )

    Thanks again!
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  2. #2
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    1. solve for what? zeros of the function?

    2. inequality problem ...

    3x/(x^2 - 4) < -1

    3x/(x^2 - 4) + 1 < 0

    3x/(x^2 - 4) + (x^2 - 4)/(x^2 - 4) < 0

    (x^2 + 3x - 4)/(x^2 - 4) < 0

    [(x+4)(x-1)]/[(x+2)(x-2)] < 0

    critical x-values are where the left side = 0 or is undefined.

    x = -4, x = 1, x = -2, and x = 2

    mark these 4 x-values on a number line ... this breaks up the x-values into 5 regions. test any x-value in each region in the above inequality.
    if the inequality is true, then all values of x in that region make the inequality true ... if false, exclude that region from the solution set.

    don't forget that x = -4 and x = 1 will be included in the solution set because they make the expression = 0.
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  3. #3
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    Red face

    thanks!

    and for #1, , yes, zeros of the function
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  4. #4
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    did you attempt the rational root theorem for #1 ?
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  5. #5
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    Talking

    lol dont worry, i checked with my teacher today, and i did the questions correctly!

    thanks for the help on #2! it really helped me ALOT!
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