What are the solutions to the equation x^5-4x^4-2x^3+4x^2+x=0 ?

The solutions to the equation x^5-4x^4-2x^3+4x^2+x=0 are x=0,x=-1,x=1,x=2+sqrt(5),x=2-sqrt(5)

Find the zeros of x^5-4x^4-2x^3+4x^2+x=0

The zeros of x^5-4x^4-2x^3+4x^2+x=0 are x=0,x=-1,x=1,x=2+sqrt(5),x=2-sqrt(5)

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x^{5} - 4 x^{4} - 2 x^{3} + 4 x^{2} + x = 0

x = 0, x = - 1, x = 1, x = 2 + 5, x = 2 - 5

Decimal Notation

x = 0, x = - 1, x = 1, x = 4.23606 \dots, x = - 0.23606 \dots

Solution steps

x^{5} - 4 x^{4} - 2 x^{3} + 4 x^{2} + x = 0

Factor

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

x (x + 1) (x - 1) (x^{2} - 4 x - 1) = 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} - 4 x - 1 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

Solve

x^{2} - 4 x - 1 = 0 : x = 2 + 5, x = 2 - 5

The solutions are

x = 0, x = - 1, x = 1, x = 2 + 5, x = 2 - 5

- x^{3} + 446.8 x^{2} + 551 x + 257.6 = 0

y, 1 + 7 x y^{4} - 3 z^{3} = 0

70 x^{3} + 24 x^{2} - 10 x + 20 = 0

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

x^{6} - 511 x^{3} = 512

What are the solutions to the equation x^5-4x^4-2x^3+4x^2+x=0 ?
The solutions to the equation x^5-4x^4-2x^3+4x^2+x=0 are x=0,x=-1,x=1,x=2+sqrt(5),x=2-sqrt(5)
Find the zeros of x^5-4x^4-2x^3+4x^2+x=0
The zeros of x^5-4x^4-2x^3+4x^2+x=0 are x=0,x=-1,x=1,x=2+sqrt(5),x=2-sqrt(5)