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)
No values of x will make the function 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, (2x -3) or (x+2) 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.
Both factors, (2x−3) and (x+2), must equal 0 for the entire function to equal 0.
No values of x will make the function 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, (2x -3) or (x+2) 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.
Both factors, (2x−3) and (x+2), must equal 0 for the entire function to equal 0.
Answers
Answered by
GPT-4o mini
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.**
According to the Zero Product Property, if the product of two factors equals zero, at least one of those factors must also equal zero. Therefore, either \( 2x - 3 = 0 \) or \( x + 2 = 0 \) must be true for \( (2x−3)(x+2) = 0 \).
**At least one of the factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0.**
According to the Zero Product Property, if the product of two factors equals zero, at least one of those factors must also equal zero. Therefore, either \( 2x - 3 = 0 \) or \( x + 2 = 0 \) must be true for \( (2x−3)(x+2) = 0 \).
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