Question: What are the <strong>UNIQUE</strong> values of a, b and c if 2 is a root of the equation ax^{2}+bx+c=0?<br>Statement I: Ratio of c to a is 1.<br>Statement II: Ratio of b to a is (-5/2).
For the next ten (10) items that follow:<br>Each item contains a Question followed by two Statements. Answer each item using the following instructions:
- A. Choose this option if the Question can be answered by one of the Statements alone but not by the other.
- B. Choose this option if the Question can be answered by either Statement alone.
- C. Choose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
- D. Choose this option if the Question cannot be answered even by using both Statements together. ✓
Correct Answer: D. Choose this option if the Question cannot be answered even by using both Statements together.
Explanation
Since 2 is a root, 4a+2b+c=0. Statement I gives c=a. Statement II gives b=-2.5a. Both together yield proportional relationships (2x^2 - 5x + 2 = 0), meaning a, b, c can take infinitely many scaled values (e.g., 4, -10, 4). <strong>UNIQUE</strong> values cannot be found.
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