Question
Based on the Zero Product Property, which of the following statements must be true about the quadratic equation (5x+1)(x−8)=0
?(1 point)
Responses
Neither of the factors, (5x+1)
or (x−8)
, must equal 0 for the left side of the equation to equal 0.
Neither of the factors, open paren 5 x plus 1 close paren or open paren x minus 8 close paren, must equal 0 for the left side of the equation to equal 0.
At least one of the factors, (5x+1)
or (x−8)
, must equal 0 for the left side of the equation to equal 0.
At least one of the factors, open paren 5 x plus 1 close paren or open paren x minus 8 close paren, must equal 0 for the left side of the equation to equal 0.
No values of x will make the left side of the equation equal 0.
No values of x will make the left side of the equation equal 0.
?(1 point)
Responses
Neither of the factors, (5x+1)
or (x−8)
, must equal 0 for the left side of the equation to equal 0.
Neither of the factors, open paren 5 x plus 1 close paren or open paren x minus 8 close paren, must equal 0 for the left side of the equation to equal 0.
At least one of the factors, (5x+1)
or (x−8)
, must equal 0 for the left side of the equation to equal 0.
At least one of the factors, open paren 5 x plus 1 close paren or open paren x minus 8 close paren, must equal 0 for the left side of the equation to equal 0.
No values of x will make the left side of the equation equal 0.
No values of x will make the left side of the equation equal 0.
Answers
GPT-4o mini
The correct statement based on the Zero Product Property is:
**At least one of the factors, (5x+1) or (x−8), must equal 0 for the left side of the equation to equal 0.**
This property states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, either \(5x + 1 = 0\) or \(x - 8 = 0\) must hold true for the equation \((5x + 1)(x - 8) = 0\) to be satisfied.
**At least one of the factors, (5x+1) or (x−8), must equal 0 for the left side of the equation to equal 0.**
This property states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, either \(5x + 1 = 0\) or \(x - 8 = 0\) must hold true for the equation \((5x + 1)(x - 8) = 0\) to be satisfied.