What are the solutions to the equation x^4+4x^3-8x=0 ?

The solutions to the equation x^4+4x^3-8x=0 are x=0,x=-2,x=-1+sqrt(5),x=-1-sqrt(5)

Find the zeros of x^4+4x^3-8x=0

The zeros of x^4+4x^3-8x=0 are x=0,x=-2,x=-1+sqrt(5),x=-1-sqrt(5)

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x^{4} + 4 x^{3} - 8 x = 0

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

Decimal Notation

x = 0, x = - 2, x = 1.23606 \dots, x = - 3.23606 \dots

Solution steps

x^{4} + 4 x^{3} - 8 x = 0

Factor

x^{4} + 4 x^{3} - 8 x : x (x + 2) (x^{2} + 2 x - 4)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x + 2 = 0 or x^{2} + 2 x - 4 = 0

Solve

x + 2 = 0 : x = - 2

Solve

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

The solutions are

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

a^{8} - 17 a^{4} + 16 = 0

24 x^{4} + 16 x^{3} - 3 x - 2 = 0

- x^{3} + 24 x^{2} - 180 x + 432 = 0

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

x^{4} x + 8 = 8 x + 16

What are the solutions to the equation x^4+4x^3-8x=0 ?
The solutions to the equation x^4+4x^3-8x=0 are x=0,x=-2,x=-1+sqrt(5),x=-1-sqrt(5)
Find the zeros of x^4+4x^3-8x=0
The zeros of x^4+4x^3-8x=0 are x=0,x=-2,x=-1+sqrt(5),x=-1-sqrt(5)