Question

Given (8x+3k)(9x−2)=0, the product of all solutions is (−3). Find k.

Answer 1

k = 36

Explanation:

Given

(8x + 3k)(9x - 2) = 0

Equate each factor to zero and solve for x

9x - 2 = 0 ⇒ 9x = 2 ⇒ x =
`(2)/(9)`

8x + 3k = 0 ⇒ 8x = - 3k ⇒ x =
`(-3k)/(8)`

The product of the solutions = - 3, thus

`(2)/(9)` × -
`(3k)/(8)` = - 3, that is

-
`(6k)/(72)` = - 3 ( multiply both sides by 72 )

- 6k = - 216 ( divide both sides by - 6 )

k = 36