InterviewSolution
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InterviewSolution
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If the equations `x^(2)+2lambdax+lambda^(2)+1=0`, `lambda in R` and `ax^(2)+bx+c=0` , where `a`, `b`, `c` are lengths of sides of triangle have a common root, then the possible range of values of `lambda` isA. `(0,2)`B. `(sqrt(3),3)`C. `(2sqrt(2),3sqrt(2))`D. `(0,oo)` |
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Answer» Correct Answer - A `(a)` `(x+lambda)^(2)+1=0` has clearly imaginery roots So, both roots of the equations are common `:. (a)/(1)=(b)/(2lambda)=(c )/(lambda^(2)+1)=k`(Say) Then `a=k`, `b=2lambdak`, `c=(lambda^(2)+1)k` As `a`, `b`, `c` are sides of triangle `a+b gt implies 2lambda+1 gt lambda^(2)+1implieslambda^(2)-2lambda lt 0` `implies lambda in (0,2)` The other conditions also imply same relation. |
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