Solve 2x^2 - 5x - 3 = 0. Which of the following lists the solutions?

Solve 2x^2 - 5x - 3 = 0. Which of the following lists the solutions?

• A. x = -3/2 or x = 1
• B. x = 0 or x = 3
• C. x = 3 or x = -1/2
• D. x = 2 or x = -1

Answer: (C)

Solving a quadratic often uses factoring when the numbers cooperate. For 2x^2 - 5x - 3, look for two numbers that multiply to (2)(-3) = -6 and add to -5. Those numbers are -6 and 1, which lets us factor as (2x + 1)(x - 3). Setting each factor to zero gives x = -1/2 or x = 3. So the solutions are x = 3 and x = -1/2, matching the choice that lists those two values. You can check quickly by substitution: 2(3)^2 - 5(3) - 3 = 0 and 2(-1/2)^2 - 5(-1/2) - 3 = 0.

Solving a quadratic often uses factoring when the numbers cooperate. For 2x^2 - 5x - 3, look for two numbers that multiply to (2)(-3) = -6 and add to -5. Those numbers are -6 and 1, which lets us factor as (2x + 1)(x - 3). Setting each factor to zero gives x = -1/2 or x = 3. So the solutions are x = 3 and x = -1/2, matching the choice that lists those two values. You can check quickly by substitution: 2(3)^2 - 5(3) - 3 = 0 and 2(-1/2)^2 - 5(-1/2) - 3 = 0.