What are the solutions to the equation x^5=5x-4x^3 ?

The solutions to the equation x^5=5x-4x^3 are x=0,x=-1,x=1,x=sqrt(5)i,x=-sqrt(5)i

Find the zeros of x^5=5x-4x^3

The zeros of x^5=5x-4x^3 are x=0,x=-1,x=1,x=sqrt(5)i,x=-sqrt(5)i

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x^{5} = 5 x - 4 x^{3}

x = 0, x = - 1, x = 1, x = 5 i, x = - 5 i

Solution steps

x^{5} = 5 x - 4 x^{3}

Move

4 x^{3}

to the left side

x^{5} + 4 x^{3} = 5 x

Move

5 x

to the left side

x^{5} + 4 x^{3} - 5 x = 0

Factor

x^{5} + 4 x^{3} - 5 x : x (x + 1) (x - 1) (x^{2} + 5)

x (x + 1) (x - 1) (x^{2} + 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x + 1 = 0 or x - 1 = 0 or x^{2} + 5 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + 5 = 0 : x = 5 i, x = - 5 i

The solutions are

x = 0, x = - 1, x = 1, x = 5 i, x = - 5 i

2 x (7 x + 1) (9 x^{2} - 25) = 0

6 x^{4} - 14 x^{2} = 0

3 x^{6} + 4 x^{4} + 4 x^{2} + 1 = 0

n^{3} - n^{2} + 15 n - 500 = 0

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

What are the solutions to the equation x^5=5x-4x^3 ?
The solutions to the equation x^5=5x-4x^3 are x=0,x=-1,x=1,x=sqrt(5)i,x=-sqrt(5)i
Find the zeros of x^5=5x-4x^3
The zeros of x^5=5x-4x^3 are x=0,x=-1,x=1,x=sqrt(5)i,x=-sqrt(5)i