What are the values for x that satisfy the equation (x + a)(x + b) = 0

What are the values for x that satisfy the equation (x + a)(x + b) = 0 ?

  1. -a and -b
  2. -a and b
  3. -ab
  4. a and -b
  5. a and b

Answer

The correct answer is A.

This problem is asking you to figure out when two quantities multiplied together can be zero. The only way two quantities can be multiplied together to get an answer of zero is if at least one of the quantities is zero.

So, either (x + a) = 0 or (x + b) = 0. The first of these equations is true when x = -a and the second when x = -b. These are the two solution values for x.

As a check, substitute -a in for x. The original equation becomes (-a + a)(-a + b), which simplifies to (0)(-a + b), and zero times anything is zero, so the original equation holds when x = -a. You can check x = -b in the similar manner.