SOLUTION: How many imaginary zeros does the function f(x) = 3x4 + 2x3 + 4x + 7 have?

By DesCarte's rule of signs:

There are no sign changes going left to right, 
so it has 0 positive zeros

Now we find f(-x)







There are 2 sign changes going left to right, 
so f(x) has either 2 negative zeros or 0 negative zeros.

A fourth degree equation has 4 zeros counting multiplicity,
and its imaginary zeros come in conjugate pairs. 

So the equation either has 2 negative zeros and one pair of
conjugate imaginary zeros or else it has 0 negative zeros
and two pairs of conjugate imaginary zeros, i.e., 4 imaginary
zeros.

Edwin