If one zeroes of the polynomial f(x) = 4x² - 8kx + 8x -9 is negative of other,
then find the zeroes of kx² + 3kx + 2.

-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.