Question 202835
Let's call the polynomial P(x). If 2 and 3i are roots of P(x) then P(x) must be:
{{{P(x) = (x -2)(x^2 + 9)}}}
If this isn't immediately clear, think about it. If 2 is a root of P(x) then, by the very definition of a root, when x = 2, P(x) = 0. Can you see that if x = 2 in the equation above, that P(x) = 0? And similarly, can you see that if x = 3i (or -3i) that P(x) is zero (because {{{x^2 + 9 = 0}}} if x = 3i (or -3i)?<br>
Now all we need to do is multiply out P(x) to see which answer is correct. we should get:
{{{x^3 - 2x^2 + 9x -18}}} so (a) is correct.