What are the solutions to the equation 12x^3-12x^2-12x=0 ?

The solutions to the equation 12x^3-12x^2-12x=0 are x=0,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2

Find the zeros of 12x^3-12x^2-12x=0

The zeros of 12x^3-12x^2-12x=0 are x=0,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2

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12 x^{3} - 12 x^{2} - 12 x = 0

x = 0, x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

Decimal Notation

x = 0, x = 1.61803 \dots, x = - 0.61803 \dots

Solution steps

12 x^{3} - 12 x^{2} - 12 x = 0

Factor

12 x^{3} - 12 x^{2} - 12 x : 12 x (x^{2} - x - 1)

12 x (x^{2} - x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{2} - x - 1 = 0

Solve

x^{2} - x - 1 = 0 : x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

The solutions are

x = 0, x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

168 x - 3 x^{2} - 3 x^{3} = 0

(x - 1)^{4} = 0

2 x^{3} + 6 x^{2} - 20 x = 0

9 x^{3} + 9 x^{2} - 25 x - 25 = 0

x^{3} + 6 x^{2} - 36 = 0

What are the solutions to the equation 12x^3-12x^2-12x=0 ?
The solutions to the equation 12x^3-12x^2-12x=0 are x=0,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2
Find the zeros of 12x^3-12x^2-12x=0
The zeros of 12x^3-12x^2-12x=0 are x=0,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2