Question

Solve the equation using the Zero-Product Property.

(3x-6)(5x+3)=0

a. 2, 3/5
b. -2, -3/5
c. 2, -3/5
d. -3, 5

Answer 1

Option (b) is correct.

Using the Zero-Product Property, on the given equation
`(3x-6)(5x+3)=0` we get,
`x=2` and
`x=(-3)/(5)`

Explanation:

Consider the given equation ,
`(3x-6)(5x+3)=0`

Zero- product property states that if the product of two term is zero then either first term is zero or second term is zero

That is
`p.q=0 \Rightarrow p=0\ \text{or} \ q=0`

Consider the given equation ,
`(3x-6)(5x+3)=0`

Applying zero-product property, we get,

`(3x-6)(5x+3)=0`

this implies that either
`(3x-6)=0` or
`(5x+3)=0`

either
`x=2` or
`x=(-3)/(5)`

Thus, using the Zero-Product Property, on the given equation
`(3x-6)(5x+3)=0` we get,
`x=2` and
`x=(-3)/(5)`.