What are the solutions to the equation 2x^3-6x^2+2x=0 ?

The solutions to the equation 2x^3-6x^2+2x=0 are x=0,x=(3+sqrt(5))/2 ,x=(3-sqrt(5))/2

Find the zeros of 2x^3-6x^2+2x=0

The zeros of 2x^3-6x^2+2x=0 are x=0,x=(3+sqrt(5))/2 ,x=(3-sqrt(5))/2

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

x = 0, x = \frac{3 + 5}{2}, x = \frac{3 - 5}{2}

Solution steps

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

Factor

2 x^{3} - 6 x^{2} + 2 x : 2 x (x^{2} - 3 x + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{2} - 3 x + 1 = 0

Solve

x^{2} - 3 x + 1 = 0 : x = \frac{3 + 5}{2}, x = \frac{3 - 5}{2}

The solutions are

x = 0, x = \frac{3 + 5}{2}, x = \frac{3 - 5}{2}

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

x^{4} - 0 x^{3} - 2 x^{2} - 0 x + 1 = 0

x^{4} - 4 x^{3} - 3 x^{2} + 10 x + 2 = 0

40000 = 17000 (1 + r)^{10}

0 = x^{3} + 5 x^{2} - 3 x - 15

What are the solutions to the equation 2x^3-6x^2+2x=0 ?
The solutions to the equation 2x^3-6x^2+2x=0 are x=0,x=(3+sqrt(5))/2 ,x=(3-sqrt(5))/2
Find the zeros of 2x^3-6x^2+2x=0
The zeros of 2x^3-6x^2+2x=0 are x=0,x=(3+sqrt(5))/2 ,x=(3-sqrt(5))/2