What are the solutions to the equation 6x^5-54x=0 ?

The solutions to the equation 6x^5-54x=0 are x=0,x=sqrt(3)i,x=-sqrt(3)i,x=-sqrt(3),x=sqrt(3)

Find the zeros of 6x^5-54x=0

The zeros of 6x^5-54x=0 are x=0,x=sqrt(3)i,x=-sqrt(3)i,x=-sqrt(3),x=sqrt(3)

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6 x^{5} - 54 x = 0

x = 0, x = 3 i, x = - 3 i, x = - 3, x = 3

Solution steps

6 x^{5} - 54 x = 0

Factor

6 x^{5} - 54 x : 6 x (x^{2} + 3) (x + 3) (x - 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x^{2} + 3 = 0 : x = 3 i, x = - 3 i

Solve

x + 3 = 0 : x = - 3

Solve

x - 3 = 0 : x = 3

The solutions are

x = 0, x = 3 i, x = - 3 i, x = - 3, x = 3

x^{3} - 2 x^{2} - 14 x + 28 = 0

x, (2 x + 1)^{4} - 80 = 1

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

x^{6} - 7 x^{3} + 10 = 0

4 x^{3} = 16 x^{2} - 48 x

What are the solutions to the equation 6x^5-54x=0 ?
The solutions to the equation 6x^5-54x=0 are x=0,x=sqrt(3)i,x=-sqrt(3)i,x=-sqrt(3),x=sqrt(3)
Find the zeros of 6x^5-54x=0
The zeros of 6x^5-54x=0 are x=0,x=sqrt(3)i,x=-sqrt(3)i,x=-sqrt(3),x=sqrt(3)