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

Find those equations whose roots are (a) reciprocal of the roots of (b) equal in magnitude but opposite in sign to the roots of the equation ax2+bx+c=0

Open in App
Solution

Let the roots of ax2+bx+c=0
be α,β and
α+β=ba,αβ=ca
(a) reciprocal roots 1α,1β
sum of roots = 1α+1β=α+βαβ=b/ac/a
=bc
and product of roots is =1α.1β=1c/a=ac
required equation is
x2(bc)x+(αac)=0
cx2+bx+a=0
(b) roots α,β
sum of roots = (α+β)=(ba)=ba
Product of roots = (α)(β)=αβ=ca
required equation is
x2(ba)x+(ca)=0
ax2bx+c=0

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