Quadratic Equations

Step 1: Identify the discriminant condition for real roots. For a quadratic equation to have real roots, the discriminant must be greater than or equal to 0.

Step 2: Apply this condition to the given equation. In the given equation , - . So, the discriminant condition is: Simplifying, we get:

Step 3: Analyze the inequality. For , is positive, and is also positive, making the inequality valid. However, for other intervals, and/or could be negative, invalidating the inequality.

Step 4: Conclusion. Therefore, the interval for is .

Step 1: Use the sum of roots formula for a quadratic equation
For a quadratic equation of the form , the sum of the roots is given by:
Step 2: Apply the formula
For the quadratic equation , we have: - , - , - .
Using the sum of roots formula:
Answer:
Therefore, the sum of the roots is . So, the correct answer is option (1).