Question

(a + 1)(a + 2) = 0
a. (1, 2)
b. (2, 1)
c. (-1, -2)
d. (-2, -1)

Explanation:

Step1: Apply Zero-Product Property

The zero - product property states that if \(AB = 0\), then either \(A=0\) or \(B = 0\) (or both). For the equation \((a + 1)(a+2)=0\), we set each factor equal to zero:

• Case 1: \(a + 1=0\). Solving for \(a\), we subtract 1 from both sides of the equation: \(a=- 1\).
• Case 2: \(a + 2=0\). Solving for \(a\), we subtract 2 from both sides of the equation: \(a=-2\).

Step2: Determine the solution set

The solutions of the equation \((a + 1)(a + 2)=0\) are \(a=-1\) and \(a = - 2\). So the solution set is \((-1,-2)\) (the order of the solutions in the set does not matter in terms of the roots of the equation, but when looking at the options, option C is \((-1,-2)\) and option D is \((-2,-1)\). Since we found the roots as \(a=-1\) and \(a=-2\), the set of solutions is \(\{-1,-2\}\) which is represented as the ordered pair (in terms of the options) \((-1,-2)\) in option C.

Answer:

C. \((-1, -2)\)