Answer:
k = 36
Step-by-step explanation:
Given
(8x + 3k)(9x - 2) = 0
Equate each factor to zero and solve for x
9x - 2 = 0 ⇒ 9x = 2 ⇒ x = [tex]\frac{2}{9}[/tex]
8x + 3k = 0 ⇒ 8x = - 3k ⇒ x = [tex]\frac{-3k}{8}[/tex]
The product of the solutions = - 3, thus
[tex]\frac{2}{9}[/tex] × - [tex]\frac{3k}{8}[/tex] = - 3, that is
- [tex]\frac{6k}{72}[/tex] = - 3 ( multiply both sides by 72 )
- 6k = - 216 ( divide both sides by - 6 )
k = 36
