InterviewSolution
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InterviewSolution
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If the roots of the equation `a(b-c)x^2+b(c-a)x+c(a-b)=0`are equal, show that `2//b=1//a+1//cdot` |
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Answer» Since the roots of the given equations are equal, its discriminant is zero, i. e., `b^(2)(c - a)^(2) - 4a(b - c) c(a - b) = 0` or `b^(2) (c^(2) + a^(2) - 2ac) - 4ac (ba - ca -b^(2) + bc) = 0` or `a^(2)b^(2) +b^(2)c^(2) + 4a^(2) c^(2) + 2b^(2)ac - 4a^(2) bc- 4abc^(2) = 0` `(ab + bc- 2ac)^(2) = 0 ` or `ab + bc -2ac = 0` or `ab + bc = 2ac` or `(1)/(c)+(1)/(a)=(2)/(b)` [dividing both sides byu abc] or `(2)/(b)=(1)/(a)+(1)/(c)` |
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