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
No values of x will make the function equal 0.
No values of x will make the function 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.
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.
At least one of the factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0.
The Zero Product Property states that if a product of two factors equals zero, then at least one of the factors must itself be zero. Therefore, the correct statement about 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 means that either (2x−3) = 0 or (x+2) = 0, or both, in order for the product to be equal to zero. Solving these individually:
If (2x−3) = 0, then 2x = 3 and x = 3/2.
If (x+2) = 0, then x = -2.
Hence, the solution to the equation (2x−3)(x+2)=0 is x = 3/2 or x = -2.