Question

Find the solution of the quadratic equation \( 2x^2 - 3x - 5 = 0 \).

• A. \( x = 1, x = -2 \)
• B. \( x = -1, x = 2 \)
• C. \( x = \frac{5}{2}, x = -1 \)
• D. \( x = \frac{-5}{2}, x = 1 \)

Hint:

Remember: The quadratic formula is used to solve any quadratic equation. Ensure to substitute the values of \( a \), \( b \), and \( c \) correctly.

Answer 1

The Correct Option is C

Step 1: Use the quadratic formula The quadratic formula is: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] For the quadratic equation \( 2x^2 - 3x - 5 = 0 \), we have: - \( a = 2 \), - \( b = -3 \), - \( c = -5 \). Step 2: Substitute the values into the quadratic formula \[ x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(2)(-5)}}{2(2)} \] \[ x = \frac{3 \pm \sqrt{9 + 40}}{4} \] \[ x = \frac{3 \pm \sqrt{49}}{4} \] \[ x = \frac{3 \pm 7}{4} \] Step 3: Solve for both values of \( x \) The two possible solutions are: \[ x_1 = \frac{3 + 7}{4} = \frac{10}{4} = 2.5 \] \[ x_2 = \frac{3 - 7}{4} = \frac{-4}{4} = -1 \] Answer: Therefore, the solutions are \( x = 2.5 \) and \( x = -1 \). So, the correct answer is option (3).