Problem: 12x cubed minus 10x squared plus 18x
how to solve
12x^3 - 10x^2 + 18x
Factor out 2x.
2x(6x^2 - 5x + 9)
If we set 2x equal to zero, we get x = 0.
When we set the remaining polynomial equal to zero,
solving with the quadratic formula, we find that
the roots are imaginary.
Let's look at the discriminant.
(b^2 - 4*a*c)
((-5)^2 - 4*6*9)
(25 - 216)
(-191)
Taking the square root of that is what produces
the imaginary numbers.
x = 0
x = 13.82i
x = -13.82i