if the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal show that a,b,c are in AP

Asked by rhinithaa | 2nd Dec, 2010, 12:24: PM

Expert Answer:

Dear Student
For the equation(b-c)x2+(c-a)x+(a-b)=0 to have equal roots Discriminant D must be zero
Let A = (b-c) B =(c-a), C = (a-b)
So B2-4AC = 0
(c-a)2 =4(b-c)(a-b)
c2+a2-2ac =4ba-4b2-4ca+4bc
4b2+c2+a2-2(2b)(c)-2(2b)(a)+2(a)(c)=0.
(c+a-2b)2=0
So 2b=c+a
or a,b,c are in AP

Answered by  | 3rd Dec, 2010, 09:52: AM

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