CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If α and β are the roots of the equation 4x25x+2=0, find the equation whose roots are
α+1α and β+1β.

A
8x2+30x+29=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
x230x+29=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
8x230x+29=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
x2+30x+29=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 8x230x+29=0
The equation is: 4x25x+2=0

Sum of the roots = 54

Product of the roots = 24=12
If the roots are α+1α,β+1β

Sum of roots = α+1α+β+1β

= α+β+α+βαβ

= 54+5412

= 54+52

154
Product of roots = (α+1α)(β+1β)

= αβ+αβ+βα+1αβ

= 12+(α+β)22αβαβ+2

= 12+2516112+2

= 12+98+2

= 4+9+168

= 298
Hence.the equation in the standard form, x2Sx+P=0 can be written as:

=x2154x+298=0

= 8x230x+29=0

Hence option C is the answer.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Algebra of Limits
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon