MEDAL & FAN ANYBODY ?
A cubic polynomial function crosses the x-axis exactly once and does not touch the x-axis except at this crossing. Which one of the following statements must be true about the function?
a. It has three unique complex roots.
b. It has three real roots, all different.
c. It has two unique real roots and one complex root.
d. It has a one real root and two complex roots or a triple real root.

Question

MEDAL & FAN ANYBODY ?
A cubic polynomial function crosses the x-axis exactly once and does not touch the x-axis except at this crossing. Which one of the following statements must be true about the function?
a. It has three unique complex roots.
b. It has three real roots, all different.
c. It has two unique real roots and one complex root.
d. It has a one real root and two complex roots or a triple real root.

welshfella · Answer

where it crosses the axis is a real root

anonymous · Answer

I would say D

welshfella · Answer

right
as its a cubic function it will have 3 roots
in this case its 1 real and 2 complex

welshfella · Answer

as a matter of interest complex roots always occur in pairs

welshfella · Answer

- so you cannot have 3 complex roots in a cubic

welshfella · Answer

so a and c are impossible
the only possible combinations are b and d

welshfella · Answer

D is correct