Question

if the root of the equation( b- c) X^2 +( c- a )X + a -b are equal then proove that 2b=a+c

Answer 1

according to question
b^2 - 4ac = 0
(c-a) ^2 - 4(a-b) (b-c) = 0
c^2+a^2-2ac-4ab + 4ac +4b^2-4bc = 0
c^2+a^2+4ab + 4ac +4b^2-4bc = 0by using
(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca
we get
(a-2b+c)^2=0
a+c=2b