Question
Based on the Zero Product Property, which of the following statements must be true about the quadratic equation iota * 0 = (z + x)(epsilon - xz) 1 point) Neither of the factors, (2x-3) or (x + 2), must equal 0 for the entire function to equal 0. Both factors, (2x-3) or (z+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, (223) or (2+2), must equal 0 for the entire function to equal 0.
Answers
GPT-4o mini
The Zero Product Property states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.
Looking at your options in light of this property:
1. **Neither of the factors, (2x-3) or (x + 2), must equal 0 for the entire function to equal 0.** - This is false because, according to the Zero Product Property, at least one of the factors must equal 0 for the product to equal 0.
2. **Both factors, (2x-3) or (x + 2), must equal 0 for the entire function to equal 0.** - This is also false, as only one factor needs to be 0 for the entire function to equal 0.
3. **No values of x will make the function equal 0.** - This is false as well since if the product is equal to zero, there must be at least one value of x that makes at least one of the factors equal to 0.
4. **At least one of the factors, (2x-3) or (x + 2), must equal 0 for the entire function to equal 0.** - This statement is true according to the Zero Product Property.
Therefore, the correct answer is:
**At least one of the factors, (2x-3) or (x + 2), must equal 0 for the entire function to equal 0.**
Looking at your options in light of this property:
1. **Neither of the factors, (2x-3) or (x + 2), must equal 0 for the entire function to equal 0.** - This is false because, according to the Zero Product Property, at least one of the factors must equal 0 for the product to equal 0.
2. **Both factors, (2x-3) or (x + 2), must equal 0 for the entire function to equal 0.** - This is also false, as only one factor needs to be 0 for the entire function to equal 0.
3. **No values of x will make the function equal 0.** - This is false as well since if the product is equal to zero, there must be at least one value of x that makes at least one of the factors equal to 0.
4. **At least one of the factors, (2x-3) or (x + 2), must equal 0 for the entire function to equal 0.** - This statement is true according to the Zero Product Property.
Therefore, the correct answer is:
**At least one of the factors, (2x-3) or (x + 2), must equal 0 for the entire function to equal 0.**