Question

the root of the equation (a-b) x square +(b -c)x(c-a) =0 are equal and prove that b+ c =2a​

Answer 1

roots of euation are equal therefore b2-4ac=0

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

(b2+C2-2bc) - 4(ac-a2-bc+ab)=0

b2+C2-2bc - 4ac-4a2+4bc-4ab=0

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

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

-2a+b+c=0

b+c=2a

Answer 2

plz refer to this attachment