Thread: f(x) and g(x) compositions

f(x) = 3x^3 - 2x^2 + x + 7

g(x) = 2x^2-4

2 QUESTIONS:


Find g of f(x)

AND...


f(x) has two complex zeros. One is in the 4th quadrant. In what quadrant is the other???

g of f(x)
= 2* (3x^3 - 2x^2 + x + 7)^2 - 4

for the second question i suggest that you use the rational root theorem to find a rational root, lets call it . we then have

where is a quadratic.

however if there is not rational root then this becomes quite difficult.

Originally Posted by Mr_Green

f(x) has two complex zeros. One is in the 4th quadrant. In what quadrant is the other???

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