use the given zero
posted by Jill on .
Use the given zero to find the remaining zeros of the function.
f(x)=x^32x^2+9x18;zero;3i
Enter the remaining zeros of f
=

The function is actually quite easy to factor using grouping
f(x_ = x^3  2x^2 + 9x  18
= x^2(x2) + 9(x2)
= (x2)(x^2+9)
so x^2 + 9 = 0 > x = ± 3i
and x2 = 0 > x = 2
the other way:
since complex roots always come in conjugate pairs
the other one had to be 3i
and its corresponding factor would have been x^2 = 9
dividing this into the f(x) function would have given us the other remaining factor of (x2) for the third root of 2