What are the solutions to the equation x^5-5x^3=36x ?

The solutions to the equation x^5-5x^3=36x are x=0,x=2i,x=-2i,x=-3,x=3

Find the zeros of x^5-5x^3=36x

The zeros of x^5-5x^3=36x are x=0,x=2i,x=-2i,x=-3,x=3

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x^{5} - 5 x^{3} = 36 x

x = 0, x = 2 i, x = - 2 i, x = - 3, x = 3

Solution steps

x^{5} - 5 x^{3} = 36 x

Move

36 x

to the left side

x^{5} - 5 x^{3} - 36 x = 0

Factor

x^{5} - 5 x^{3} - 36 x : x (x^{2} + 4) (x + 3) (x - 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Solve

x + 3 = 0 : x = - 3

Solve

x - 3 = 0 : x = 3

The solutions are

x = 0, x = 2 i, x = - 2 i, x = - 3, x = 3

x^{4} - 8 x^{3} + 16 x^{2} = 0

x^{3} - 17 x - 4 = 0

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

2 x^{3} + (- 7) x^{2} + 6 x + 5 = 0

b^{3} = 1331

What are the solutions to the equation x^5-5x^3=36x ?
The solutions to the equation x^5-5x^3=36x are x=0,x=2i,x=-2i,x=-3,x=3
Find the zeros of x^5-5x^3=36x
The zeros of x^5-5x^3=36x are x=0,x=2i,x=-2i,x=-3,x=3