What are the solutions to the equation x^2-x^3=12 ?

The solutions to the equation x^2-x^3=12 are x=-2,x= 3/2+i(sqrt(15))/2 ,x= 3/2-i(sqrt(15))/2

Find the zeros of x^2-x^3=12

The zeros of x^2-x^3=12 are x=-2,x= 3/2+i(sqrt(15))/2 ,x= 3/2-i(sqrt(15))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

x = - 2, x = \frac{3}{2} + i \frac{15}{2}, x = \frac{3}{2} - i \frac{15}{2}

Solution steps

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

Move

12

to the left side

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

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

Factor

- x^{3} + x^{2} - 12 : - (x + 2) (x^{2} - 3 x + 6)

- (x + 2) (x^{2} - 3 x + 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 2 = 0 or x^{2} - 3 x + 6 = 0

Solve

x + 2 = 0 : x = - 2

Solve

x^{2} - 3 x + 6 = 0 : x = \frac{3}{2} + i \frac{15}{2}, x = \frac{3}{2} - i \frac{15}{2}

The solutions are

x = - 2, x = \frac{3}{2} + i \frac{15}{2}, x = \frac{3}{2} - i \frac{15}{2}

8 x^{3} - 98 x = 0

x^{4} - 16

x^{4} - 16 x^{2} + 75 = 2 x^{2} - 6

9 x^{5} = 27 x^{3}

4 x^{3} - 9 x^{2} - 1 = 0

What are the solutions to the equation x^2-x^3=12 ?
The solutions to the equation x^2-x^3=12 are x=-2,x= 3/2+i(sqrt(15))/2 ,x= 3/2-i(sqrt(15))/2
Find the zeros of x^2-x^3=12
The zeros of x^2-x^3=12 are x=-2,x= 3/2+i(sqrt(15))/2 ,x= 3/2-i(sqrt(15))/2