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Math Help - tan²x+4tanx+1=0 help!!

  1. #1
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    tan²x+4tanx+1=0 help!!

    Helppp! tan²x+4tanx+1=0 [0,2pi)
    How do you do it? I tried factorising it which isn't possible.
    so i used -b+-squareroot of(b^2-4ac)
    which got me stuck at (-4 plusminus squareroot of 12 ) / 2
    i don't know what to do next.
    thanksss
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  2. #2
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    Hello, leo037!

    \tan^2\!x+4\tan x+1\:=\:0

    I tried factorising it which isn't possible.

    So i used the Quadratic Formula
    which got me stuck at: . \frac{-4 \pm\sqrt{12}}{2} \:=\:-2 \pm\sqrt{3}

    i don't know what to do next.
    I used my calculator . . .

    x \;=\;\tan^{-1}(\text{-}2+\sqrt{3}) \:=\:\text{-}\,\frac{\pi}{12}\;\;(\text{-}15^o)

    x \;=\;\tan^{-1}(\text{-}2-\sqrt{3}) \;=\;\text{-}\,\frac{5\pi}{12}\;\;(\text{-}75^o)

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