Question

What are the solutions of 3(x – 4)(2x - 3) = 0? Check all that apply.
-4,-3,-2/3,3/2,3,4 ????

Answer 1

4 and 3/2

Explanation:

The zero product property states that for the product of any numbers and polynomials (which here would be 3, x-4, and 2x-3), if any of the numbers of polynomials are equal to 0 then the entire expression is equal to 0.

In this case, that means that if 3, x-4, or 2x-3 is equal to 0 then they are a solution (the whole expression equal 0).

For the first: 3 can never be equal to 0

2nd: x-4=0 ⇒ (add 4) x=4

3rd: 2x-3=0 ⇒ (add 3) 2x=3 ⇒ (divide by 2) x=3/2

Therefore:

The possible solutions are 4 and 3/2