Question

Which correctly describes the root of the following cubic equation? x^3-3x^2+4x-12=0

Answer 1

The equation has one real root and two complex roots.

Explanation:

The given equation is

`x^3-3x^2+4x-12=0`

The above equation is true form x=3, therefore (x-3) is a factor of above equation.

Use long division or synthetic division method to divide the equation by (x-3).

`(x-3)(x^2+4)=0`

Equate each factor equal to zero.

`x-3=0`

`x=3`

Therefore 3 is a real root of the equation.

`x^2+4=0`

`x^2=-4`

`x=√(-4)`

`x=\pm 2i`

2i and -2i are complex roots of the equation.

Therefore the equation has one real root and two complex roots.