Question 20

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

To find the solutions to the equation (x-2)(x+4) = 0, we set each factor equal to zero. This gives us the solutions x - 2 = 0, resulting in x = 2, and x + 4 = 0, resulting in x = -4.

A) -4 and 2

This option is correct because setting (x-2) = 0 gives x = 2, and setting (x+4) = 0 gives x = -4. Therefore, both values satisfy the original equation, confirming that -4 and 2 are indeed the solutions.

B) -3 and 1

This option is incorrect as substituting x = -3 into the equation results in (-3-2)(-3+4) = (-5)(1) = -5, which does not equal zero. Substituting x = 1 gives (1-2)(1+4) = (-1)(5) = -5, also not zero.

C) -2 and 4

This option is incorrect because substituting x = -2 results in (-2-2)(-2+4) = (-4)(2) = -8, which does not satisfy the equation. Similarly, substituting x = 4 gives (4-2)(4+4) = (2)(8) = 16, also not zero.

D) -1 and 1

This option is incorrect as substituting x = -1 yields (-1-2)(-1+4) = (-3)(3) = -9, which does not equal zero. For x = 1, substituting gives (1-2)(1+4) = (-1)(5) = -5, also not satisfying the equation.

E) -1 and 3

This option is incorrect. Substituting x = -1 results in (-1-2)(-1+4) = (-3)(3) = -9, which is not zero. For x = 3, we have (3-2)(3+4) = (1)(7) = 7, also not zero.

Conclusion

The correct solution, -4 and 2, matches the conditions set by the equation (x-2)(x+4) = 0, as both values yield results that satisfy the equation. All other options fail to produce solutions that equal zero when substituted back into the equation. Thus, A is definitively the right answer.