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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- Jul 7th 2009, 05:17 AMhiemmerFinding 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 - Jul 7th 2009, 05:22 AMalexmahone
$\displaystyle 12x^3+12x^2+12x=0$

$\displaystyle 12x(x^2+x+1)=0$

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

$\displaystyle x=0$ or $\displaystyle x=\frac{-1\pm i\sqrt3}{2}$ - Jul 7th 2009, 05:22 AMartvandalay11
- Jul 7th 2009, 05:25 AMskeeter
- Jul 7th 2009, 08:13 AMSean12345
Or if you're not a fan of the quadratic formula (I never was), you could complete the square on the quadratic giving,

$\displaystyle

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

$