What are the solutions to the equation x^3-12x+11=0 ?

The solutions to the equation x^3-12x+11=0 are x=1,x=(-1+3sqrt(5))/2 ,x=(-1-3sqrt(5))/2

Find the zeros of x^3-12x+11=0

The zeros of x^3-12x+11=0 are x=1,x=(-1+3sqrt(5))/2 ,x=(-1-3sqrt(5))/2

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x^{3} - 12 x + 11 = 0

x = 1, x = \frac{- 1 + 3 5}{2}, x = \frac{- 1 - 3 5}{2}

Decimal Notation

x = 1, x = 2.85410 \dots, x = - 3.85410 \dots

Solution steps

x^{3} - 12 x + 11 = 0

Factor

x^{3} - 12 x + 11 : (x - 1) (x^{2} + x - 11)

(x - 1) (x^{2} + x - 11) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} + x - 11 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + x - 11 = 0 : x = \frac{- 1 + 3 5}{2}, x = \frac{- 1 - 3 5}{2}

The solutions are

x = 1, x = \frac{- 1 + 3 5}{2}, x = \frac{- 1 - 3 5}{2}

7 x^{3} - x^{2} - 7 x + 1

4 s^{3} + 15 s^{2} + 18 s + 5 = 0

x^{4} + 5 x^{2} = 6

2 x^{3} - 7 x^{2} - 5 x + 4 = 0

7 x^{3} - 2 x^{2} - 35 x + 10 = 0

What are the solutions to the equation x^3-12x+11=0 ?
The solutions to the equation x^3-12x+11=0 are x=1,x=(-1+3sqrt(5))/2 ,x=(-1-3sqrt(5))/2
Find the zeros of x^3-12x+11=0
The zeros of x^3-12x+11=0 are x=1,x=(-1+3sqrt(5))/2 ,x=(-1-3sqrt(5))/2