Question: What is the other root of the quadratic equation with real coefficients if one of the roots is \frac{-4-\sqrt{10}}{2}?<br>Statement-I:<br>The product of the roots is -\frac{3}{2}(3+\sqrt{10}).<br>Statement-II:<br>The sum of roots of quadratic equation is -1.

Consider the following for the next ten (10) items that follow :<br>Mark option (a) if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.<br>Mark option (b) if the question can be answered by using either statement alone.<br>Mark option (c) if the question can be answered by using both the statements together, but cannot be answered using either statement alone.<br>Mark option (d) if the question cannot be answered even by using both the statements together.

  1. A. The question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
  2. B. The question can be answered by using either statement alone ✓
  3. C. The question can be answered by using both the statements together, but cannot be answered using either statement alone
  4. D. The question cannot be answered even by using both the statements together

Correct Answer: B. The question can be answered by using either statement alone

Explanation

Let the roots be r_1 and r_2, with r_1 = \frac{-4-\sqrt{10}}{2}. From Statement-I: r_1 \times r_2 = \text{Product}. We can solve for r_2 directly. Thus, Statement-I alone is sufficient. From Statement-II: r_1 + r_2 = -1. We can solve for r_2 = -1 - r_1. Thus, Statement-II alone is also sufficient.

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