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Math Help - Finding zeros of a polynomial

  1. #1
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    Finding zeros of a polynomial

    How can I find the zeros(other than 0 itself) of this polynomial?

    y = 12x^3 + 12x^2 + 12x

    thank you in advance
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  2. #2
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    12x^3+12x^2+12x=0

    12x(x^2+x+1)=0

    x=0 or x=\frac{-1 \pm \sqrt{1-4}}{2}

    x=0 or x=\frac{-1\pm i\sqrt3}{2}
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  3. #3
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    Quote Originally Posted by hiemmer View Post
    How can I find the zeros(other than 0 itself) of this polynomial?

    y = 12x^3 + 12x^2 + 12x

    thank you in advance
    Factor out 12x, so y=12x(x^2+x+1)=0
    and now you can see x=0 is a solution and you can use the quadratic formula for x^2+x+1
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  4. #4
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    Quote Originally Posted by hiemmer View Post
    How can I find the zeros(other than 0 itself) of this polynomial?

    y = 12x^3 + 12x^2 + 12x

    thank you in advance
    12x^3 + 12x^2 + 12x = 0

    12x(x^2 + x + 1) = 0

    x = 0 , use the quadratic formula to find the other two roots ...

    x = \frac{-1 \pm i\sqrt{3}}{2}
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  5. #5
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    Or if you're not a fan of the quadratic formula (I never was), you could complete the square on the quadratic giving,

     <br />
x^2+x+1=\left(x+\frac{1}{2}\right)^2+\frac{3}{4}=0<br />
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