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If one root of the equation `x^(2)+px+q=0` is `2+sqrt(3)` where `p, q epsilon I` and roots of the equation `rx^(2)+x+q=0` are `tan 268^(@)` and `cot 88^(@)` then value of `p+q+r` is :A. `-1`B. `-2`C. `-3`D. `-4` |
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Answer» Correct Answer - B If one root of ………… `x^(2)+px+q=0` has one root `2+sqrt(3)` then other root `= 2 - sqrt(3)` "sum" of roots `= - (P)/(1)= 2+sqrt(3)+2-sqrt(3)` `implies P = -4` product of roots `= (q)/(1) = (2+sqrt(3))(2-sqrt(3))` `implies q = 1` …..(i) product of roots `= (q)/(1) = (2+sqrt(3))(2-sqrt(3))` `implies q=1` ....(ii) now `rx^(2)+x+q=0` roots are tan `(268^(@)) tan (180^(@)+88^(@)) = tan 88^(@)` and `cot 88^(@)` `:.` Product of roots `= tan 88^(@) .cot 88^(@) = (q)/(r )` `implies 1 = (q)/(r ) implies q = r` ....(iii) `:. p+q+r= -4+1+1= -2` |
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