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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