Question

"What is the solution set of the equation (x-a)(x+b)=0?"

Please select the correct option from the following choices:
a) (A, -b)
b) (-a, -b)
c) (-a, b)
d) (A, b)

Answer 1

The solution set of the equation (x-a)(x+b)=0 is given by the values that make each factor zero individually, resulting in x=a and x=-b, thus the solution set is (a, -b).

Step-by-step explanation:

The solution set of the equation (x-a)(x+b)=0 is determined by observing that a product of two factors is zero if and only if at least one of the factors is zero. Thus, there are two possibilities for the variable x:

• x - a = 0, which leads to x = a
• x + b = 0, which leads to x = -b

Hence, the solution set for the equation is the set of values (a, -b), which makes option a) the correct choice.