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Reviewed CSCA Mathematics question · Easy

Solve the inequality (x - 1)(x + 4) ≤ 0. Which of the following is the solution set?

  1. (-∞, -4] ∪ [1, ∞)
  2. [-4, 1]
  3. (-∞, -4]
  4. [1, ∞)
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].

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