What are the solutions to the equation x^3-x^2+12=0 ?

The solutions to the equation x^3-x^2+12=0 are x=-2,x= 3/2+i(sqrt(15))/2 ,x= 3/2-i(sqrt(15))/2

Find the zeros of x^3-x^2+12=0

The zeros of x^3-x^2+12=0 are x=-2,x= 3/2+i(sqrt(15))/2 ,x= 3/2-i(sqrt(15))/2

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

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

Solution steps

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}

u^{3} - 13.2 = - 11.8

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

8 x^{3} - 46 x^{2} + 31 x - 5 = 0

(x - 2)^{4} - (x - 2)^{2} - 6 = 0

5 x^{3} + 5 x^{2} - 4 x - 4

What are the solutions to the equation x^3-x^2+12=0 ?
The solutions to the equation x^3-x^2+12=0 are x=-2,x= 3/2+i(sqrt(15))/2 ,x= 3/2-i(sqrt(15))/2
Find the zeros of x^3-x^2+12=0
The zeros of x^3-x^2+12=0 are x=-2,x= 3/2+i(sqrt(15))/2 ,x= 3/2-i(sqrt(15))/2