Question

(a-b)x2+(b-c)x+(c-a) have equal root .Prove 2a=b+c

Answer 1

Here is your answer ...please mark as the brainliest answer

Answer 2

b^2-4ac=0

(b-c)^2-4(a-b)(c-a)=0

b^2-2bc+c^2-4(ac-a^2+bc+ba)=0

b^2-2bc+c^2-4ac+4a^2+4bc+4ba=0

4a^2+b^2+c^2+4ab+2bc-4ac=0(which is of the form(a^2 +b^2+c^2+2ab+2bc+2ca)

so,[(2a)^+(-b)^2+(-c)+2(2a)(-c)+2(-b)(-c)+2(2a)(-c)=0

(2a-b-c)^2=0

on equating,

2a-b-c=0

on trasposing

2a=b+c