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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3 x^{3} + 8 x^{2} - 1 = 0

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

Decimal Notation

x = 0.33333 \dots, x = - 0.38196 \dots, x = - 2.61803 \dots

Solution steps

3 x^{3} + 8 x^{2} - 1 = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Solve

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

The solutions are

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

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

(1 - r)^{3} = 3 - 3 r

x^{3} - 5 x^{2} + 4 x + 10 = 0

x^{6} - 22 x^{3} + 49 = 0

5 x^{3} - 125 x^{5} = 0

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