Question 40

The solutions of (x - 2)(x + 4) = 0 are -2 and 4.

To solve the equation (x - 2)(x + 4) = 0, we set each factor equal to zero, resulting in the solutions x = 2 and x = -4. Therefore, the correct solutions are -2 and 4.

A) 4 and 2

This option incorrectly lists the solutions as 4 and 2. While 4 is one of the solutions, 2 is not a solution of the equation; instead, the correct solution includes -4.

B) -3 and 1

This option presents entirely incorrect values. Neither -3 nor 1 is derived from solving the equation (x - 2)(x + 4) = 0.

C) -2 and 4

This option correctly identifies the solutions of the equation. Setting (x - 2) = 0 gives x = 2 and (x + 4) = 0 gives x = -4, leading to the conclusion that the solutions are indeed -2 and 4.

D) -1 and 1

This option is also incorrect. The values -1 and 1 do not satisfy the equation, as they do not result from solving the factors of the equation (x - 2)(x + 4) = 0.

E) 0-1 and 3

This option is incorrect as well. The values 0-1 and 3 do not correspond to any solutions from the equation provided, as they do not come from the factors of (x - 2) and (x + 4).

Conclusion

The correct answer is definitively C, as it reflects the accurate solutions derived from the factors of the equation (x - 2)(x + 4) = 0. Options A, B, D, and E fail to provide the correct values obtained by applying the zero product property, confirming C as the only valid answer.