solve each polynomial?

4x^2-121=0

3x^4+12x^3-3x^2=12x

x^4+x^3-x^2-x=0

8x^3-27=0

Find the answers and I would like you to show your work. Will pick best answer ASAP.

1 Answer

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  • 8 years ago
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    1)

    4x^2 -121 = 0

    4x^2 = 121

    x^2 = 30.25

    x = 5.5, -5.5

    2)

    3x^4 + 12x^3 - 3x^2 = 12x

    Right away we realize there is an 'x' term on every side so we can divide by an x and drop one

    3x^3 + 12x^2 - 3x = 12

    3x^3 + 12x^2 - 3x - 12 = 0

    3x^2(x + 4) -3(x+4) = 0

    (3x^2-3) (x+4) = 0

    3x^2 - 3 = 0

    3x^2 = 3

    x^2 = 1

    x = +/- 1

    x+4 = 0

    x = -4

    so our roots are (-1,1,-4)

    3)

    x^4+x^3-x^2-x = 0

    x(x^3+x^2-x-1) = 0

    x^3+x^2-x-1 = 0

    x^2 (x+1) -1(x+1) = 0

    (x^2-1) (x+1) = 0

    x = -1,1

    4)

    8x^3 - 27 = 0

    8x^3 = 27

    x^3 = 27/8

    x = (27/8) ^ (1/3) (cube rooted)

    x = 1.5

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