g of f(x)
= 2* (3x^3 - 2x^2 + x + 7)^2 - 4
Two observations:
The question states there are only two complex zeros.
f(x) is a cubic polynomial so there can be at most two complex zeros.
Either way you look at it, there are ONLY two complex zeros of f(x). Since f(x) is a polynomial with real coefficients the two complex zeros are complex conjugates of each other.
Since one complex zero is in the 4th quadrant, it must have the form a - bi, where a, b > 0. Since the other zero is the complex conjugate of this, the second zero is of the form a + bi, which would be in the first quadrant.
-Dan