Consider a question and two statements:<br>Question: Does the equation ax^2+bx+c=0 have real roots of opposite sign?<br>Statement-I: The discriminant D \gt 0<br>Statement-II: c/a \gt 0<br>Which one of the following is correct in respect of the question and the statements?
- A. Statement-I alone is sufficient to answer the question
- B. Statement-II alone is sufficient to answer the question
- C. Both Statement-I and Statement-II are together sufficient to answer the question ✓
- D. Both Statement-I and Statement-II are not sufficient to answer the question
Correct Answer: C. Both Statement-I and Statement-II are together sufficient to answer the question
Explanation
For the roots to have opposite signs, their product \frac{c}{a} must be negative. Statement II says \frac{c}{a} \gt 0, meaning roots have the same sign (if they are real). Statement I confirms the roots are real. Both are required to definitively answer that the roots do not have opposite signs.
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