if roots of equation (a-b)x2+(b-c)x+(c-a)=0,prove that b+c=2a\xa0

1.	if roots of equation (a-b)x2+(b-c)x+(c-a)=0,prove that b+c=2a\xa0
Answer» ttttttttjj from The question must be, if roots of equation (a-b)x2+(b-c)x+(c-a)=0 are equal , prove that b+c = 2a.Using Discriminant,D = B2-4AC as compared with the general quadratic equation Ax2+Bx+C=0so, A = a-b\xa0B = b-cC = c-aFor roots to be equal, D=0(b-c)2\xa0- 4(a-b)(c-a) =0b2+c2-2bc -4(ac-a2-bc+ab) =0b2+c2-2bc -4ac+4a2+4bc-4ab=04a2+b2+c2+2bc-4ab-4ac=0(2a-b-c)2=0i.e. 2a-b-c =02a= b+c

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