What are the solutions to the equation x^5+x^3-6x=0 ?

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

Find the zeros of x^5+x^3-6x=0

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

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

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

Solution steps

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

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

x^{5} = - 32

(1 + \frac{x}{3})^{8} = 1.276

x, 3 y^{3} = 4 x^{3} + 1

x^{3} + x^{2} - x + 1 = 0

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