Question

If the roots of the equation (b-c)x2+(c-a)x+(a-b)=0 are equal ,accordingly prove that 2b=a+c

Answer 1

general form is Ax² + Bx + C= 0
if A + B + C = 0 
then zeroes of polynomial are 1 and C/A
here A + B + C = b -c +c - a + a - b = 0
therefore zeroes are 1 and (a - b) / (b - c)
its given that they are equal
∴ (a - b) / (b - c) = 1
⇒a - b = b - c
2b = a + c
hence proved
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Answer 2

plz refer to this attachment