Find the solution set of the inequality 2x^2 + x - 6 < 0.
Show the answer and explanation
Correct answer
A. (-2, 3/2)
Principle or equation
To solve a quadratic inequality, factor the quadratic expression, find the roots, and test intervals on the number line.
Why this answer is correct
Factor 2x^2 + x - 6 = (2x - 3)(x + 2). Roots are x = 3/2 and x = -2. The parabola opens upward, so the expression is negative between the roots. Thus the solution is (-2, 3/2).
Example
Solve x^2 - 4 < 0: (x - 2)(x + 2) < 0, roots -2 and 2, solution (-2, 2).
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