Quadratic Equation

Step 1: Concept
For the equation , let the roots be and .
Step 2: Analysis
The sum of roots and the product of roots .
Step 3: Evaluation
Since , it follows that and . The discriminant , which is greater than 0 for .
Step 4: Conclusion
Because the sum, product, and discriminant are all positive, the equation has real and positive roots.
Final Answer: (c)

Step 1: Understanding the Concept:
Consider the function . If we can find two points where takes the same value, then by Rolle's theorem, there exists a point where which is exactly the given quadratic.

Step 2: Detailed Explanation:
Let . Then . Also, . Thus, . By Rolle's theorem, there exists at least one such that . But . Hence, the quadratic has a root in (0,1).

Step 3: Final Answer:
The root lies in the interval (0, 1), which corresponds to option (A).