tanA,tanB,tanc are the roots of the eqn. x3-k2x2-px+2k+1=0,then triangle abc will be a triangle of what nature?explain the ans?
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1 Answers
24tanA+tanB+tanC>0
since A+B+C=pi
=> tanA.tanB.tanC >0
SO 2 cases come
a) Tow factors negative and one factor positive
b) All three factors postive
but tan takes negative value when pi>angle >pi/2 which is not possible (two angles cant be obtuse)
=> case a) rejected
=> all three factors positve
=> A,B,C <Ï€/2
=> acute
