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.
3x24x+1=0, from a quadratic equation whose roots are α2β and β2α.

Open in App
Solution

Since α,β are are the roots of the equation 3x24x+10.
we have α+β=43,αβ=13
Now, for the required equation, the sum of the roots =(α2β+β2α)=α3+β3αβ
=(α+β)33αβ(α+β)αβ=(43)33×13×4313=289
Also, product of the roots =(α2β)(β2α)=αβ=13
The required equation is x2289x+13=0 or 9x229x+3=0

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