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

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

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

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

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

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

Decimal Notation

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

Solution steps

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

Factor

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

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

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 = 2 + 5, x = 2 - 5

4 x^{4} - 65 x^{2} = 16

12 x^{3} - 12 x^{2} - 24 x = 0

x^{4} + 5 x^{2} + 16 = 0

x^{3} + x^{2} - 18 = 0

x^{7} = x + 1

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