Question

(b-c)squre of x+ (c-a) x+(a-b) =0 two roots of equal of this equation then prove that 2b=a+c​

Answer 1

(b-c)² + (c-a)x + (a-b) = 0

A= b-c

B= c-a

C= a-b

This equation has equal roots

So, Discriminant = 0

D=B²-4AC=0

D=(c-a)²−4(b-c)(a-b)=0

D=(c²+a²−2ac)-4(ba-ac-b²+bc)=0

D=c²+a²−2ac-4ab+4ac+4b²-4bc=0

c²+a²+2ac-4b(a+c)+4b²=0

(a+c)²-4b(a+c)+4b²=0

[(a+c)-2b]²=0

a+c=2b

Hope this helps