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

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

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

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

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

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

Decimal Notation

x = 1, x = 2.41421 \dots, x = - 0.41421 \dots

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} - 2 x - 1 = 0

Solve

x - 1 = 0 : x = 1

Solve

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

The solutions are

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

8 x^{4} - 32 x^{2} = 0

x^{3} + x^{2} - x + 15 = 0

x^{3} - 12 x^{2} + 47 x - 60 = 0

3 q^{3} = - 8 + \frac{D}{A}

x^{3} - 15 x^{2} + 56 x = 0

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