If the roots of equation `a(b-c)x^2+b(c-a)x+c(a-b)=0` be equal prove that `a,b,c` are in H.P.

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If the roots of equation `a(b-c)x^2+b(c-a)x+c(a-b)=0` be equal prove that `a,b,c` are in H.P. If the roots of equation `a(b-c)x^2+b(c-a)x+c(a-b)=0` be equal prove that `a,b,c` are in H.P.
Show that the roots of the equation `a(b-c)x^2+b(c-a)x+c(a-b)=0` are equal if a,b,c are in H.P. Show that the roots of the equation `a(b-c)x^2+b(c-a)x+c(a-b)=0` are equal if a,b,c are in H.P.
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