What are the solutions to the equation roots x^5+x^3-6x ?

The solutions to the equation roots x^5+x^3-6x are x=0,x=-sqrt(2),x=sqrt(2),x=sqrt(3)i,x=-sqrt(3)i

Find the zeros of roots x^5+x^3-6x

The zeros of roots x^5+x^3-6x are x=0,x=-sqrt(2),x=sqrt(2),x=sqrt(3)i,x=-sqrt(3)i

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roots

x^{5} + x^{3} - 6 x

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

Solution steps

x^{5} + x^{3} - 6 x

The roots are the intercepts with the x-axis

(y = 0)

x^{5} + x^{3} - 6 x = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 2 = 0 : x = - 2

Solve

x - 2 = 0 : x = 2

Solve

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

The solutions are

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

z^{4} = - 16 i

x^{3} - 2 x^{2} - x + 2

12 x^{4} + 64 x^{3} + 59 x^{2} - 23 x - 12 = 0

x^{3} = 40

(2 x^{2} - 5 x + 1)^{2} - 16 x^{2} + 40 x - 1 = 0

What are the solutions to the equation roots x^5+x^3-6x ?
The solutions to the equation roots x^5+x^3-6x are x=0,x=-sqrt(2),x=sqrt(2),x=sqrt(3)i,x=-sqrt(3)i
Find the zeros of roots x^5+x^3-6x
The zeros of roots x^5+x^3-6x are x=0,x=-sqrt(2),x=sqrt(2),x=sqrt(3)i,x=-sqrt(3)i