What are the solutions to the equation 2x^3-12x^2+8x=0 ?

The solutions to the equation 2x^3-12x^2+8x=0 are x=0,x=3+sqrt(5),x=3-sqrt(5)

Find the zeros of 2x^3-12x^2+8x=0

The zeros of 2x^3-12x^2+8x=0 are x=0,x=3+sqrt(5),x=3-sqrt(5)

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2 x^{3} - 12 x^{2} + 8 x = 0

x = 0, x = 3 + 5, x = 3 - 5

Decimal Notation

x = 0, x = 5.23606 \dots, x = 0.76393 \dots

Solution steps

2 x^{3} - 12 x^{2} + 8 x = 0

Factor

2 x^{3} - 12 x^{2} + 8 x : 2 x (x^{2} - 6 x + 4)

2 x (x^{2} - 6 x + 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{2} - 6 x + 4 = 0

Solve

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

The solutions are

x = 0, x = 3 + 5, x = 3 - 5

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

x^{5} - 2 x^{4} - x + 2 = 0

x^{4} - 7 x^{2} = - 6

4 x^{4} - 9 x^{2} - 9 = 0

2 x^{3} - 4 x^{2} - 30 x = 0

What are the solutions to the equation 2x^3-12x^2+8x=0 ?
The solutions to the equation 2x^3-12x^2+8x=0 are x=0,x=3+sqrt(5),x=3-sqrt(5)
Find the zeros of 2x^3-12x^2+8x=0
The zeros of 2x^3-12x^2+8x=0 are x=0,x=3+sqrt(5),x=3-sqrt(5)