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)

Question

Responses

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) or ​(x+2), must equal 0 for the entire function to equal 0.
Neither 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) or ​(x+2), must equal 0 for the entire function to equal 0.
Both 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.

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.

Answer 1

The Zero Product Property states that if a product of factors equals zero, then at least one of the factors must be zero. Applying this to the quadratic equation (2x−3)(x+2)=0, it means that for the function to equal 0, at least one of the factors must be zero.

Therefore, the correct statement is:

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

This means that either 2x−3 = 0 or x+2 = 0. Solving these gives the values of x that satisfy the equation:

For 2x−3 = 0:
2x = 3
x = 3/2 or 1.5

For x+2 = 0:
x = -2

These are the two values of x that make the function equal to 0.