Question

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

• A. \( \frac{3}{2} \)
• B. \( \frac{5}{2} \)
• C. \( \frac{-5}{2} \)
• D. \( \frac{-3}{2} \)

Hint:

The sum of the roots of a quadratic equation is \( -\frac{b}{a} \).

Answer 1

The Correct Option is A

Step 1: Use the sum of roots formula for a quadratic equation For a quadratic equation \( ax^2 + bx + c = 0 \), the sum of the roots is given by: \[ \text{Sum of roots} = -\frac{b}{a} \] Step 2: Apply the formula For the quadratic equation \( 2x^2 - 3x - 5 = 0 \), we have: - \( a = 2 \), - \( b = -3 \), - \( c = -5 \). Using the sum of roots formula: \[ \text{Sum of roots} = -\frac{-3}{2} = \frac{3}{2} \] Answer: Therefore, the sum of the roots is \( \frac{3}{2} \). So, the correct answer is option (1).