Discussion

Explanation:

Since α, ß are roots of the equation 3x2 – 4x – 6 = 0

∴ α + ß = 43 and αß = - 63 = - 2

Now QE whose roots are α2 + 1 and ß2 + 1 can be formed as

x2 - (sum of the roots)x + (product of the roots)
∴ x2 – (α2 + 1 + ß2 + 1) + (α2 + 1)(ß2 + 1)

Now,
⇒ α2 + 1 + ß2 + 1 = (α + ß)2 – 2αß + 2
= 169 + 4 + 2 = 169 + 6 = 709

and (α2 + 1)(ß2 + 1) = α2ß2 + (α2 + ß2) + 1 = (αß)2 + (α + ß)2 - 2αß + 1
= 4 + 169 + 4 + 1 = 169 + 9 = 979

∴ The required equation is 
x2 - 709x + 979 = 0

⇒ 9x2 - 70x + 97 = 0

Hence, option (b).

» Your doubt will be displayed only after approval.


Doubts


Feedback

Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.


© 2024 | All Rights Reserved | Apti4All