Answer:
imaginary roots
Step-by-step explanation:
For a quadratic in the form ...
[tex]ax^2+bx+c=0[/tex]
the discriminant is ...
[tex]d=b^2-4ac[/tex]
You have a=1, b=-6, c=12, so the discriminant is ...
d = (-6)² -4(1)(12) = 36 -48 = -12
When the discriminant is negative, both roots are complex. When the discriminant is not a perfect square, both roots are irrational. Here, the discriminant is negative and not a perfect square, so the roots are complex with an irrational imaginary part.
The best single descriptor is imaginary root.
_____
The roots are (-b±√d)/(2a) = (6 ± 2i√3)/2 = 3 ± i√3. These roots have a rational real part and an irrational imaginary part. When the number with an imaginary part has a non-zero real part, it is called "complex", rather than "imaginary."
