What are the solutions to the equation 3x^3-24x^2+54x=0 ?

The solutions to the equation 3x^3-24x^2+54x=0 are x=0,x=4+sqrt(2)i,x=4-sqrt(2)i

Find the zeros of 3x^3-24x^2+54x=0

The zeros of 3x^3-24x^2+54x=0 are x=0,x=4+sqrt(2)i,x=4-sqrt(2)i

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3 x^{3} - 24 x^{2} + 54 x = 0

x = 0, x = 4 + 2 i, x = 4 - 2 i

Solution steps

3 x^{3} - 24 x^{2} + 54 x = 0

Factor

3 x^{3} - 24 x^{2} + 54 x : 3 x (x^{2} - 8 x + 18)

3 x (x^{2} - 8 x + 18) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{2} - 8 x + 18 = 0

Solve

x^{2} - 8 x + 18 = 0 : x = 4 + 2 i, x = 4 - 2 i

The solutions are

x = 0, x = 4 + 2 i, x = 4 - 2 i

x^{3} - 2 x^{2} - 15 x + 36 = 0

r^{5} = 32

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

2 x^{4} + 9 x^{2} = 68

0 = 9 y - y^{3}

What are the solutions to the equation 3x^3-24x^2+54x=0 ?
The solutions to the equation 3x^3-24x^2+54x=0 are x=0,x=4+sqrt(2)i,x=4-sqrt(2)i
Find the zeros of 3x^3-24x^2+54x=0
The zeros of 3x^3-24x^2+54x=0 are x=0,x=4+sqrt(2)i,x=4-sqrt(2)i