Midpoint Summative Practice Exam

Solve x^2 - 4x - 5 = 0.

x = -1 x = 5 x = 0 x = 5 or x = -1

Correct Answer:

x = 5 or x = -1

Explanation:

Solving a quadratic by factoring means finding two numbers that multiply to the constant term and add to the coefficient of x. Here, we want two numbers that multiply to -5 and add to -4. Those numbers are -5 and +1, since (-5)(1) = -5 and (-5) + 1 = -4. This lets us factor the expression as (x − 5)(x + 1) = 0. By the zero-product property, either x − 5 = 0 or x + 1 = 0, giving x = 5 or x = −1. Both values satisfy the equation, so the solution set is x = 5 or x = −1. (Using the quadratic formula would also yield the same results: x = (4 ± 6)/2, which gives 5 and −1.)

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