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

Question

?(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.

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.
Neither of the factors, left parenthesis 2 x minus 3 right parenthesis nor 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.

Answer 1

Based on the Zero Product Property, the correct statement regarding the quadratic equation \((2x−3)(x+2)=0\) is:

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

This is because the Zero Product Property states that if the product of two factors equals zero, at least one of those factors must be zero.