Question
Download Solution PDFComprehension
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 statements is correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given:
⇒ a2 (b2 – c 2 ) x2 + b 2 (c 2 – a 2 ) x + c 2 (a 2 – b 2 ) = 0...(i)
Now Equation has equal roots:
Then D =0
⇒ [b2 (c 2 – a2 )]2 – 4a 2 c 2 (b 2 – c 2 ) (a 2 – b 2 ) = 0
⇒ b4 (c 2 – a 2 )2 – 4a 2 c 2 (b 2 – c 2 ) (a 2 – b 2 ) = 0
Solving above equation, we get
⇒ b4 (c2 + a2 )2 = 4a 4 c 4
⇒ b 2 (a 2 + c 2 ) = 2a 2 c 2
⇒ \(\frac{2}{b^2} = \frac{1}{a^2}+ \frac{1}{c^2}\)
⇒ a2 , b 2 and c 2 are in HP
∴ Option (c) is correct.
Last updated on May 30, 2025
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