Question

if the roots of a(b-c)x2+b(c-a)x+c(a-b) are equal then show that 1/a+1/c=2/b

Answer 1

if the roots are equal then D=0 that is (c-a)-4(b-c)(a-b)=0pn further expanding we will get
(2b-(a+C))^2=0
i.e. 2b=a+c
no
1/a+1/c=2(1/b)because (2b=a+c)
THUS I/a+1/b+1/c are in ap