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

Let x3+ax2+bx+c=0 has roots α,β,γ. If α+2=1α2,β+2=1β2 and γ+2=1γ2, then the value of 3a+2b+c is

Open in App
Solution

As the given relation is
α+2=1α2α3+2α21=0 (1)
Similarly,
β3+2β21=0 (2)
γ3+2γ21=0 (3)
From equations (1),(2) and (3), we have
x3+2x21=0 (4)
And α,β,γ are the roots of equation (4).

Now, x3+ax2+bx+c=0 has roots α,β,γ, so on comparing this equation with eq. (4), we get
a=2,b=0,c=1
3a+2b+c=5

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