How do you use a graphing utility to approximate the solutions of #2tan^2x+7tanx-15=0# in the interval #[0,2pi)#?

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Answer 1 · 2018-08-09T15:55:53

#= 56.31^o, 101.39^o, 236.31^o, 281.39^o in [ 0, 360^o ]#

Solving the quadratic equation,

#tan x = 1/4( - 7 +- sqrt( 7^2+4(2)(15)) = 1/4( - 7 +- 13 ) #

#= - 5, 1.5#.

x = { kpi + arctan ( - 5 )}, {kpi + arctan ( 1.5 )}, k = 0, +-1, +-2, ...#

#= { k180^o- 78.69^o }, {k180^o + 56.31^o }#

#= ( ....101.39^o, 281.39^o... ), ( 56.31^o, 236.31^o..)#

#= 56.31^o, 101.39^o, 236.31^o, 281.39^o in [ 0, 360^o ]#