What are the solutions to the equation x^3+3x^2-3x-1=0 ?

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

Find the zeros of x^3+3x^2-3x-1=0

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

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

x = 1, x = - 2 + 3, x = - 2 - 3

Decimal Notation

x = 1, x = - 0.26794 \dots, x = - 3.73205 \dots

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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 + 3, x = - 2 - 3

The solutions are

x = 1, x = - 2 + 3, x = - 2 - 3

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

(x - 5) (x^{2} - 4) = 0

x^{3} - 9 x^{2} - 81 x = - 729

x^{4} - 12 8^{\frac{13}{5}} = 0

2 x^{4} + 3 x^{2} + 8 = 0

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