Answer:
-1 and -2
Step-by-step explanation:
f(x) = 4x² − 8kx + 8x −9
f(x) = 4x² − 8(k−1)x − 9
If one root of f(x) is the opposite of the other, then f(x) must be a difference of squares, which means -8(k−1) = 0.
-8(k−1) = 0
k = 1
Therefore, the other polynomial is:
x² + 3x + 2
(x + 1) (x + 2)
The zeros are -1 and -2.
