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

The solutions to the equation -3x^3+2x^2+1=0 are x=1,x=-1/6+i(sqrt(11))/6 ,x=-1/6-i(sqrt(11))/6

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

The zeros of -3x^3+2x^2+1=0 are x=1,x=-1/6+i(sqrt(11))/6 ,x=-1/6-i(sqrt(11))/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

x = 1, x = - \frac{1}{6} + i \frac{11}{6}, x = - \frac{1}{6} - i \frac{11}{6}

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

3 x^{2} + x + 1 = 0 : x = - \frac{1}{6} + i \frac{11}{6}, x = - \frac{1}{6} - i \frac{11}{6}

The solutions are

x = 1, x = - \frac{1}{6} + i \frac{11}{6}, x = - \frac{1}{6} - i \frac{11}{6}

x^{3} + 2 x = 1

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

3 x^{4} + 6 x^{2} + 1 = 0

x^{3} - 10 x - 24 = 0

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

What are the solutions to the equation -3x^3+2x^2+1=0 ?
The solutions to the equation -3x^3+2x^2+1=0 are x=1,x=-1/6+i(sqrt(11))/6 ,x=-1/6-i(sqrt(11))/6
Find the zeros of -3x^3+2x^2+1=0
The zeros of -3x^3+2x^2+1=0 are x=1,x=-1/6+i(sqrt(11))/6 ,x=-1/6-i(sqrt(11))/6