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Math Help - Determining x-intercepts of polynomial function

  1. #1
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    Determining x-intercepts of polynomial function

    How do you determine the x-intercepts of the polynomial function y = -(2x+5)^3 - 20

    I did this:

    0 = -(2x+5)^3 - 20

    20 = -2x+5)^3

    -5 3sqrt(20/-2) (3 before the sqrt being the little 3)

    x= 10.7

    The answer should be -3.86 however.
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    Quote Originally Posted by Devi09 View Post
    How do you determine the x-intercepts of the polynomial function y = -(2x+5)^3 - 20

    I did this:

    0 = -(2x+5)^3 - 20

    20 = -2x+5)^3

    -5 3sqrt(20/-2) (3 before the sqrt being the little 3)

    x= 10.7

    The answer should be -3.86 however.


    Hi Devi09,

    See if you can follow this:

    -(2x+5)^3-20=0

    -(2x+5)^3=20

    -(2x+5)=\sqrt[3]{20}

    -2x-5=\sqrt[3]{20}

    -2x=\sqrt[3]{20}+5

    x=\dfrac{\sqrt[3]{20}+5}{-2}


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  3. #3
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    Quote Originally Posted by Devi09 View Post
    How do you determine the x-intercepts of the polynomial function y = -(2x+5)^3 - 20

    I did this:

    0 = -(2x+5)^3 - 20

    20 = -2x+5)^3
    You've dropped a "(". It should be 20= -(2x+5)^3. Now "undo" that. -20^{1/3}= 2x+ 5
    2x= -20^{1/3}- 5, x= (-20^{1/3})/2

    -5 3sqrt(20/-2) (3 before the sqrt being the little 3)
    "cube root" or "cbrt" not "square root" nor "3sqrt"
    But your real error is that you divided by two before taking the cuberoot. You must take the cuberoot first because the "2x+ 5" is inside the cube.

    x= 10.7

    The answer should be -3.86 however.
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