Question

If the roots of the quadratic equation (a-b)x²+ (b-C) x + (c-a) = 0 are equal.Prove that 2a= b+c​

Answer 1

Answer:

If the quadratic equation ax²+bx+c=0

whose roots are equal then it's

deteminant is equal to zero.

(a-b)x²+(b-c)x+(c-a)=0

Deteminant =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

Therefore,

b+c=2a

Hence proved.

I hope this help.

Answer 2

Answer:

2a= b+c is the correct answer.

Hope it helps