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

a) three real roots each with a different value
b) one real root and two complexroots
c) three real roots, two of which are equal in value
d) two real roots and one complex root

Question

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

a) three real roots each with a different value
b) one real root and two complexroots
c) three real roots, two of which are equal in value
d) two real roots and one complex root

anonymous · Answer

I know that the factors of 12 are 1, 2, 3, 4, 6, and 12

anonymous · Answer

Therefore, the possible roots are 1, 2, 3, 4, 6, and 12

anonymous · Answer

does it help to know that it is 
$$(x-3)(x^2+4)$$?

anonymous · Answer

actually there are more possible rational zeros, also the negative of what you wrote above
a rather large total, and there is no guarantee that the zeros are even rational, although they are in this example

anonymous · Answer

(x-3)(x^2+4)

Okay, so for (x-3), x=3?

anonymous · Answer

Because x^2+4=0 creates x^2=-4, does this mean that there is one real root and two complex roots?

anonymous · Answer

@jdoe0001