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Use the quadratic formula to find all solutions in the interval [0,2pi): tan^2x-6tanx+4=0

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1 Answer

 Tan^2 X + 6 Tan X + 4 =0
 
 
   Tan X = - 6/2 ± √ (6^2 -16)
                               2
 
              = -3 ± √5
 
                Tan X = -3 + √5       X = - 0.65 rad = -0.21 π  or  X = 0.79 π
       Tan  X = -3 - √5    X = -1.38 rad= -0.44π
       or  X = π - 0.44 π = 0.56π