What is the general solution for tan^2(θ)+5tan(θ)+2=0 ?

The general solution for tan^2(θ)+5tan(θ)+2=0 is θ=-0.41320…+pin,θ=-1.35498…+pin

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tan^2(θ)+5tan(θ)+2=0

tan^{2} (θ) + 5 tan (θ) + 2 = 0

θ = - 0.41320 \dots + πn, θ = - 1.35498 \dots + πn

Solution steps

tan^{2} (θ) + 5 tan (θ) + 2 = 0

Solve by substitution

tan (θ) = \frac{- 5 + 17}{2}, tan (θ) = \frac{- 5 - 17}{2}

tan (θ) = \frac{- 5 + 17}{2} : θ = arctan (\frac{- 5 + 17}{2}) + πn

tan (θ) = \frac{- 5 - 17}{2} : θ = arctan (\frac{- 5 - 17}{2}) + πn

Combine all the solutions

θ = arctan (\frac{- 5 + 17}{2}) + πn, θ = arctan (\frac{- 5 - 17}{2}) + πn

Show solutions in decimal form

θ = - 0.41320 \dots + πn, θ = - 1.35498 \dots + πn

cos (z) = - 2

sin (2 x) = sin (x), x, \in [0, 2 π]

cos (2 x) + cos (- x) = 0

2 sin^{2} (u) - 3 cos (u) = 0

sin (2 t) = sin (t)

What is the general solution for tan^2(θ)+5tan(θ)+2=0 ?
The general solution for tan^2(θ)+5tan(θ)+2=0 is θ=-0.41320…+pin,θ=-1.35498…+pin