How do you solve 2tan^2x+4tanx-3=0?

1 Answer
Nghi N.
Nov 4, 2015

Solve 2tan^2 x + 4tan x - 3 = 0

Ans: 30.16; 210.16; -68.82 and 111.18

Explanation:

Call tan x = t. Solve the quadratic equation:
2t^2 + 4t - 3 = 0
D = d^2 = b^2 - 4ac = 16 + 24 = 40 --> d = +- 2sqrt10.
t = -4/4 +- 2sqrt10/4 = -1 +- sqrt10/2 = (-2 +- sqrt10)/2

a. t = tan x = (-2 + sqrt10)/2 = 1.16/2 = 0.58
tan x = 0.58 --> x = 30^@16 and x = 30.16 + 180 = 210^@16

b. t = tan x = (-2 - sqrt10)/2 = -5.16/2 = -2.58
tan x = -2.58 -> x = -68^@82 and x = - 68.82 + 180 = 111^@18

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