InterviewSolution
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InterviewSolution
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Let `a`, `b`, `c` and `m in R^(+)`. The possible value of `m` (independent of `a`, `b` and `c`) for which atleast one of the following equations have real roots is `{:(ax^(2)+bx+cm=0),(bx^(2)+cx+am=0),(cx^(2)+ax+bm=0):}}`A. `(1)/(2)`B. `(1)/(8)`C. `(1)/(12)`D. `(1)/(4)` |
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Answer» Correct Answer - B::C::D `(b,c,d)` If at least one of the equations has real roots, then `D_(1)+D_(2)+D_(3) ge 0` `(b^(2)-5acm)+(c^(2)-4bam)+a^(2)-4cbm ge 0` `a^(2)+b^(2)+c^(2) ge 4(ab+bc+ca)m` `4m ge (a^(2)+b^(2)+c^(2))/(ab+bc+ca)`………`(1)` `AA a,b,c in R+` but `a^(2)+b^(2) ge 2ab` etc. `:. a^(2)+b^(2)+c^(2) ge ab+bc+ca` `(a^(2)+b^(2)+c^(2))/(ab+bc+ca) ge 1` `:.(a^(2)+b^(2)+c^(2))/(ab+bc+ca)|_(min)=1` , Hence `4m` must be less than or equal to the minimum value. `:. 4m le 1` gtbrgt `implies m le (1)/(4)` `implies m in (0,(1)/(4)]` |
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