Comprehension

Direction : Consider the following for the items that follow :  

The roots of the quadratic equation 

a2(b2 - c2)x2 + b2(c2 - a2)x + c2(a2 - b2) = 0 are equal (a2 ≠ b2 ≠ c2).

Which one of the following is a root of the equation? 

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. \(\rm \frac{b^2(c^2-a^2)}{a^2(c^2-b^2)}\)
  2. \(\rm \frac{b^2(c^2-a^2)}{a^2(b^2-c^2)}\)
  3. \(\rm \frac{b^2(c^2-a^2)}{2a^2(c^2-b^2)}\)
  4. \(\rm \frac{b^2(c^2-a^2)}{2a^2(b^2-c^2)}\)

Answer (Detailed Solution Below)

Option 3 : \(\rm \frac{b^2(c^2-a^2)}{2a^2(c^2-b^2)}\)
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Detailed Solution

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Explanation:

Let α be the required root.

Sum of roots = \(\frac{-B}{A} = \frac{-b^2(c^2-a^2)}{a^2(b^2-c^2)}\)

⇒ α + α = \( = \frac{-b^2(c^2-a^2)}{a^2(b^2-c^2)}\)

⇒ α = \( \frac{b^2(c^2-a^2)}{2a^2(c^2-b^2)}\)

∴ Option (c) is correct

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