Algebra> Sir how to do this que. I tried bt its to...

Sir how to do this que. I tried bt its too long... so any short trick is thr???

Mithu , 8 Years ago

Grade 12

1 Answers

Ajay

Last Activity: 8 Years ago

None of the options given as answers are correct, but below is short way to solve the question..........................................

$Let\quad \alpha \quad be\quad the\quad fourth\quad root\quad of\quad equation\\ since\quad tanA,\quad tanB,\quad tanC\quad and\quad \alpha \quad are\quad roots\quad of\quad equation\quad we\quad have.\\ tanA+tanB+tanC+\alpha \quad =\quad p---(1)\\ tanA.tanB.tanC.\alpha \quad =\quad s\quad -----(2)\\ \quad Also\quad A+B+C\quad =\quad 180\\ \quad \quad \quad \quad \quad tan(A+B)\quad =\quad Tan(180-C)\quad =\quad -TanC\\ \quad \quad \quad \quad \quad \frac { tanA+tanB }{ 1-tanA.tanB } \quad =\quad -tanC\\ \quad \quad tanA.tanB.tanC\quad =\quad tanA+tanB+tanC----(3)\\ From\quad 1\quad 2\quad and\quad 3\\ \quad s/\alpha \quad =\quad p-\alpha \quad \\ { \alpha }^{ 2 }-p\alpha +s\quad =\quad 0\\ \alpha \quad =\quad \frac { p\pm \sqrt { { p }^{ 2 }-4s } }{ 2 }$