What are the solutions to the equation 4x^3-12x^2+6x=0 ?

The solutions to the equation 4x^3-12x^2+6x=0 are x=0,x=(3+sqrt(3))/2 ,x=(3-sqrt(3))/2

Find the zeros of 4x^3-12x^2+6x=0

The zeros of 4x^3-12x^2+6x=0 are x=0,x=(3+sqrt(3))/2 ,x=(3-sqrt(3))/2

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4 x^{3} - 12 x^{2} + 6 x = 0

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

Decimal Notation

x = 0, x = 2.36602 \dots, x = 0.63397 \dots

Solution steps

4 x^{3} - 12 x^{2} + 6 x = 0

Factor

4 x^{3} - 12 x^{2} + 6 x : 2 x (2 x^{2} - 6 x + 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

2 x^{2} - 6 x + 3 = 0 : x = \frac{3 + 3}{2}, x = \frac{3 - 3}{2}

The solutions are

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

(- 2 x^{2} - 5 x + 3) (3 a + x) = 0

a^{3} = 78

x^{4} - 6 x^{3} + 14 x^{2} - 14 x + 5 = 0

3 x^{5} - 20 x^{3} = 0

3 x^{3} + x^{2} - 8 x + 4 = 0

What are the solutions to the equation 4x^3-12x^2+6x=0 ?
The solutions to the equation 4x^3-12x^2+6x=0 are x=0,x=(3+sqrt(3))/2 ,x=(3-sqrt(3))/2
Find the zeros of 4x^3-12x^2+6x=0
The zeros of 4x^3-12x^2+6x=0 are x=0,x=(3+sqrt(3))/2 ,x=(3-sqrt(3))/2