What are the solutions to the equation 9x^3-12x^2-8x-1=0 ?

The solutions to the equation 9x^3-12x^2-8x-1=0 are x=-1/3 ,x=(5+sqrt(37))/6 ,x=(5-sqrt(37))/6

Find the zeros of 9x^3-12x^2-8x-1=0

The zeros of 9x^3-12x^2-8x-1=0 are x=-1/3 ,x=(5+sqrt(37))/6 ,x=(5-sqrt(37))/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

9 x^{3} - 12 x^{2} - 8 x - 1 = 0

x = - \frac{1}{3}, x = \frac{5 + 37}{6}, x = \frac{5 - 37}{6}

Decimal

x = - 0.33333 \dots, x = 1.84712 \dots, x = - 0.18046 \dots

Solution steps

9 x^{3} - 12 x^{2} - 8 x - 1 = 0

Factor

9 x^{3} - 12 x^{2} - 8 x - 1 : (3 x + 1) (3 x^{2} - 5 x - 1)

(3 x + 1) (3 x^{2} - 5 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

3 x + 1 = 0 : x = - \frac{1}{3}

Solve

3 x^{2} - 5 x - 1 = 0 : x = \frac{5 + 37}{6}, x = \frac{5 - 37}{6}

The solutions are

x = - \frac{1}{3}, x = \frac{5 + 37}{6}, x = \frac{5 - 37}{6}

4 x^{3} - x^{2} + 36 - 9 x = 0

20 x^{3} - 48 x^{2} + 24 x = 0

x^{3} - 6 x^{2} - 7 x + 60 = 0

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

30 x^{500} = 40 x

What are the solutions to the equation 9x^3-12x^2-8x-1=0 ?
The solutions to the equation 9x^3-12x^2-8x-1=0 are x=-1/3 ,x=(5+sqrt(37))/6 ,x=(5-sqrt(37))/6
Find the zeros of 9x^3-12x^2-8x-1=0
The zeros of 9x^3-12x^2-8x-1=0 are x=-1/3 ,x=(5+sqrt(37))/6 ,x=(5-sqrt(37))/6