Question

If root of a quadratic eqn (a-b)x square +(b-c )x+(c-a)=0 are equal. prove that 2a=b+c.

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Answer 1

Answer:

ANSWER

Given,  (a−b)x2+(b−c)x+(c−a)=0  are equal.

Then the discriminant =0.

Then 

(b−c)2−4(c−a)(a−b)=0

or, (b2−2bc+c2)−4(ac−bc−a2+ab)=0

or, (b2+2bc+c2)−2a(b+c)+4a2=0

or, (b+c)2−2a(b+c)+4a2=0

or, (b+c−2a)2=0

or, 2a=b+c.