Solve the inequality (x - 1)(x + 4) ≤ 0. Which of the following is the solution set?
Show the answer and explanation
Correct answer
B. [-4, 1]
Principle or equation
For a quadratic inequality in factored form, the sign of the product changes at the roots. The product is non-positive between the roots if the leading coefficient is positive.
Why this answer is correct
The roots are x = -4 and x = 1. Test intervals: for x < -4, product positive; for -4 < x < 1, product negative; for x > 1, product positive. Since the inequality is ≤ 0, include the roots. Thus the solution is [-4, 1].
Example
For (x - 2)(x + 3) ≤ 0, roots are -3 and 2; the solution is [-3, 2].
This published item includes a stored explanation and passed the platform’s publication workflow. It is independent preparation material, not a claim of an official or recalled examination question.