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InterviewSolution
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If the roots of the equation `(b-c)x^2+(c-a)x+(a-b)=0` are equal then `a,b,c` will be in |
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Answer» Give equation is `a(b-c)x^(2)+b(c-a)x+c(a-b)=0`…………i Here, coefficient of `x^(2)+` coefficient of `x+` constant term `=0` i.e. `a(b-c)+b(c-a)+c(a-b)=0` The, 1 is a root of Eq. (i) Since, its roots are equal. Therefore its other root will be also equal to 1. Then product of roots `=1xx1=(c(a-b))/(a(b-c))` `impliesab-ac=ca-bc` `:.b=(2ac)/(a+c)` Hence a,b,c are in HP. |
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