Solve the equation 2x^2 + x - 6 = 0.

• A. x = 3/2 or x = -2
• B. x = -3/2 or x = 2
• C. x = 3 or x = -2/3
• D. x = -3 or x = 2/3

Answer: (D)

This quadratic is solved by factoring and using the zero-product property. Look for two numbers that multiply to a*c = 2(-6) = -12 and add to b = 1. Those numbers are 4 and -3. So 2x^2 + x - 6 becomes 2x^2 + 4x - 3x - 6. Factor by grouping: 2x(x + 2) - 3(x + 2) = (2x - 3)(x + 2). Set each factor to zero: 2x - 3 = 0 or x + 2 = 0. This gives x = 3/2 or x = -2. Both values satisfy the equation, as a quick check shows.