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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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 = 3.85410 \dots, x = - 2.85410 \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}

2 (x^{2} - 36) (x^{2} + 49) = 0

x^{3} - 5 x^{2} - x - 1 = 0

x^{3} - 4 x^{2} + 7 x - 1 = 0

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

x (x + 3) (x - 1) = 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