Question: What is the other root of the quadratic equation with real coefficients if one of the roots is \(\frac{-4-\sqrt{10}}{2}\) ?

Statement-I: The product of the roots is \(-\frac{3}{2}(3+\sqrt{10})\)

Statement-II: The sum of roots of quadratic equation is -1.

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CDS Elementary Mathematics 3 Sep 2023 Official Paper
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  1. if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
  2. if the question can be answered by using either statement alone.
  3. if the question can be answered by using both the statements together, but cannot be answered using either statement alone.
  4. if the question cannot be answered even by using both the statements together.

Answer (Detailed Solution Below)

Option 2 : if the question can be answered by using either statement alone.
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Detailed Solution

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Given:

One of the roots is  \(\frac{-4-\sqrt{10}}{2}\) 

Statement-1 The product of the roots is \(-\frac{3}{2}(3+\sqrt{10})\)

Statement-2 The sum of roots of the quadratic equation is -1.

Calculation:

According to the first statement

Let, the other root = a

⇒ a ×  \(\frac{-4-\sqrt{10}}{2}\)  = \(-\frac{3}{2}(3+\sqrt{10})\)

⇒ a = \(-\frac{3}{2}(3+\sqrt{10})\) × \(\frac{2}{-4-\sqrt{10}}\) 

This means the first statement is sufficient to answer.

According to the second statement

Let, the other root = a

⇒  \(\frac{-4-\sqrt{10}}{2}\) + a = -1

⇒ a = -1 -(\(\frac{-4-\sqrt{10}}{2}\))

This means the second statement is sufficient to answer.

∴ The correct answer is option 2

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