Question
Download Solution PDFQuestion: 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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
Last updated on May 29, 2025
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