Answer:
roots are ...
Step-by-step explanation:
The equation can be factored by grouping:
(12x^3 -9x^2) +(4x -3) = 0
3x^2(4x -3) +(4x -3) = 0
(3x^2 +1)(4x -3) = 0
The equation has roots that are the values of x making these factors zero:
3x^2 +1 = 0
x^2 = -1/3 = -3/9
x = ±(i/3)√3
and
4x -3 = 0
4x = 3
x = 3/4
The one real root is x = 3/4; the two complex roots are ±√3/3.
