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

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.

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.
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.

Answer 1

Bot GPT 4-o mini answered
2 hours ago

The correct statement based on the Zero Product Property 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, then at least one of those factors must be equal to zero. In this case, if \((2x−3)(x+2)=0\), then either \(2x−3=0\) or \(x+2=0\) (or both) must be true.