Question

Based on the Zero Product Property, which of the following statements must be true about the quadratic equation (2x−3)(x+2)=0
?(1 point)
Responses

At least one of the factors, (2x−3)
or ​(x+2)
, must equal 0 for the entire function to equal 0.
At least one of the factors, left parenthesis 2 x minus 3 right parenthesis or left parenthesis x plus 2 right parenthesis , must equal 0 for the entire function to equal 0.

Both factors, (2x−3)
and ​(x+2)
, must equal 0 for the entire function to equal 0.
Both factors, left parenthesis 2 x minus 3 right parenthesis and left parenthesis x plus 2 right parenthesis , must equal 0 for the entire function to equal 0.

No values of x will make the function equal 0.
No values of x will make the function equal 0.

Neither of the factors, (2x−3)
nor ​(x+2)
, must equal 0 for the entire function to equal 0.

Answer 1

"At least one of the factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0."

Reason: By the Zero Product Property, if a product equals 0 then at least one factor is 0. Here that gives 2x−3=0 ⇒ x=3/2 or x+2=0 ⇒ x=−2 (they cannot be zero at the same time).