wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If α,β are the roots of the equation 2x23x6=0, then the equation whose roots are α21 and β21 is

A
4x225x+7=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
4x217x+7=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2x225x7=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
2x217x+7=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 4x225x+7=0
Let α21=yα=±y+1

Now, α is the root of the equation 2x23x6=0, so
2α23α6=0
2(±y+1)23(±y+1)6=0
2y+26=(±3y+1)
2y4=(±3y+1)
Squaring on both sides, we get
4y216y+16=9(y+1)
4y225y+7=0

Hence, the required equation is 4x225x+7=0



flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Transformation of Roots: Algebraic Transformation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon