Question

if the roots of the equation (a-b)x²+(bc)x+ (c-a)= 0 are equal then prove that 2a= b+c

Answer 1

ots an easy Q just put formula of D and put 0 on rhs...thats it...
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.
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Answer 2

plz refer to this attachment