We know that,
If the quadratic equation ax²+bx+c=0
Whose roots are equal then it’s deteminant is equal to zero
We have, (a-b)x²+(b-c)x+(c-a)=0
Deteminant = D= b² -4ac = 0
(b-c)² -4(a-b)(c-a)=0
b²+c²-2bc-4ac+4a²+4bc-4ab=0
b²+c²+4a²+4bc-4ac-4ab=0
b²+c²+(-2a)²+2bc+2c(-2a)+2(-2a)b=0
(b+c-2a)²=0
b+c-2a=0
b+c=2a
Hence proved.
More Articles