Solve 2x² − 5x − 12 = 0.

Correct answer: x = 4, x = −3/2. Factorise: 2x² − 8x + 3x − 12 = 2x(x − 4) + 3(x − 4) = (2x + 3)(x − 4), so x = 4 or x = −3/2.

Background: Split the middle term −5x into −8x + 3x.

• x = −4, x = −3/2: x = −4 does not satisfy the equation.
• x = −3/2, x = −4: x = −4 does not satisfy the equation.
• None of these: “None of these” is incorrect because x = 4 and x = −3/2 are correct.

Did you know? Check: 2(16) − 20 − 12 = 0.

Memory trick: Product ac = −24; sum = −5.