Question

Find the sum of the roots of the quadratic equation $ 2x^2 - 5x + 3 = 0 $.

• A. \( \frac{5}{2} \)
• B. \( \frac{3}{2} \)
• C. \( \frac{7}{2} \)
• D. \( \frac{1}{2} \)

Hint:

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

Answer 1

The Correct Option is A

Step 1: Apply the sum of roots formula for quadratic equations
A quadratic equation in the form \( ax^2 + bx + c = 0 \) has roots whose sum is calculated using: \[ \text{Sum of roots} = -\frac{b}{a} \]
Step 2: Execute the formula
Given the quadratic equation \( 2x^2 - 5x + 3 = 0 \), the coefficients are identified as: - \( a = 2 \), - \( b = -5 \), - \( c = 3 \). 
Applying the sum of roots formula: \[ \text{Sum of roots} = -\frac{-5}{2} = \frac{5}{2} \] 
Conclusion:
Consequently, the sum of the roots equals \( \frac{5}{2} \). This corresponds to option (1).