InterviewSolution
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InterviewSolution
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Let `f(x)=ax^(2)+bx+c`, `g(x)=ax^(2)+px+q`, where `a`, `b`, `c`, `q`, `p in R` and `b ne p`. If their discriminants are equal and `f(x)=g(x)` has a root `alpha`, thenA. `alpha` will be `A.M.` of the roots of `f(x)=0`, `g(x)=0`B. `alpha` will be `G.M.` of the roots of `f(x)=0`, `g(x)=0`C. `alpha` will be `A.M.` of the roots of `f(x)=0` or `g(x)=0`D. `alpha` will be `G.M.` of the roots of `f(x)=0` or `g(x)=0` |
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Answer» Correct Answer - A `(a)` `a alpha^(2)+b alpha+c=a alpha^(2)+p alpha+q=0` `implies alpha=(q-c)/(b-p)`…………`(i)` and `b^(2)-4ac=p^(2)-4aq` `impliesb^(2)-p^(2)=4a(c-q)` `implies b+q=(4a(c-q))/(b-p)=-4a alpha` (from `(i)`) `:.alpha=(-(b+p))/(4a)=((-b)/(a)-(p)/(a))/(4)` which is `AM` of all the roots of `f(x)=0` and `g(x)=0` |
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