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InterviewSolution
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If `x_(1)` and `x_(2)` are the arithmetic and harmonic means of the roots fo the equation `ax^(2)+bx+c=0`, the quadratic equation whose roots are `x_(1)` and `x_(2)` isA. `abx^(2)+(b^(2)+ac)x+bc=0`B. `2abx^(2)+(b^(2)+4ac)x+2bc=0`C. `2abx^(2)+(b^(2)+ac)x+bc=0`D. none of these |
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Answer» Correct Answer - B Let `alpha` and beta` be the roots of `ax^(2)+bx+c=0` `:.x_(1)=(alpha+beta)/2=-b/(2a)` and `x_(2)=(2alpha beta)/(alpha+betsa)=(2 . c/a)/(-b/a)=-(2c)/b` `:.` The required equation is `x^(2)-[(-b/(2a))+(-(2c)/b)]x+(2bc)/(2ab)=0` i.e. `2abx^(2)+(b^(2)+4ac)x+2bc=0` |
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