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

The solutions to the equation x^5-6x^3+5x=0 are x=0,x=-1,x=1,x=-sqrt(5),x=sqrt(5)

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

The zeros of x^5-6x^3+5x=0 are x=0,x=-1,x=1,x=-sqrt(5),x=sqrt(5)

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

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

Decimal Notation

x = 0, x = - 1, x = 1, x = - 2.23606 \dots, x = 2.23606 \dots

Solution steps

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

Factor

x^{5} - 6 x^{3} + 5 x : x (x + 1) (x - 1) (x + 5) (x - 5)

x (x + 1) (x - 1) (x + 5) (x - 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 + 5 = 0 or x - 5 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

Solve

x + 5 = 0 : x = - 5

Solve

x - 5 = 0 : x = 5

The solutions are

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

x, x^{3} + 2 x^{2} + 5 x = 0

5000 = 1000 (1 + x)^{12}

x^{4} + 22 x - 24 = 0

4 x^{4} - 5 x^{2} + 9 = 0

x^{81} x^{2} - 4 = 0

What are the solutions to the equation x^5-6x^3+5x=0 ?
The solutions to the equation x^5-6x^3+5x=0 are x=0,x=-1,x=1,x=-sqrt(5),x=sqrt(5)
Find the zeros of x^5-6x^3+5x=0
The zeros of x^5-6x^3+5x=0 are x=0,x=-1,x=1,x=-sqrt(5),x=sqrt(5)