Question

If p ,q and r are rational numbers and p ≠ q ≠ r, then 1 root of the equation: (p2 − q2 )x2 − (q2 − r2 )x + (r2 − p2 ) = 0 are: (a) p/q , r/p (b) p2 /q2 , r2 /q2 (c) 1, p2−q2 /r2−p2 (d) −1, p2−r2 /p2−q2

Please Answer

Answer 1

Given :   (p² − q² )x² − (q² − r² )x + (r² − p² ) = 0  

To find : root of the equation

Solution:

(p² − q² )x² − (q² − r² )x + (r² − p² ) = 0

if x  =  1

=> (p² − q²)  -  (q² − r² ) +  (r² − p² )  = 2(r² - q²)  q ≠ r   hence not equal to zero

if x = - 1

=>  (p² − q²)  +  (q² − r² ) +  (r² − p² )  = 0

Hence one root is  - 1

products of roots =  (r² − p² ) /  (p² − q² )

Hence another root = -   (r² − p² ) /  (p² − q² )

= (p² − r² ) /  (p² − q² )

Hence option d is correct

- 1 ,    (p² − r² ) /  (p² − q² )    are the roots

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Answer 2

Answer:

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