Answer:
The equation has one real root and two complex roots.
Step-by-step 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.
\(x^2+4=0\)
\(x^2=-4\)
\(x=\sqrt{-4}\)
\(x=\pm 2i\)
2i and -2i are complex roots of the equation.
Therefore the equation has one real root and two complex roots.
