SOLUTION: Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a graphing utility to approximate the angle x. (Enter your answers as a comma-separated list.

Algebra ->  Trigonometry-basics -> SOLUTION: Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a graphing utility to approximate the angle x. (Enter your answers as a comma-separated list.      Log On


   

Question 1038841: Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a graphing utility to approximate the angle x. (Enter your answers as a comma-separated list. Round each answer to four decimal places.)
tan^2 x + 5 tan x + 3 = 0
Answer by ikleyn(52790) About Me  (Show Source):
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Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a graphing utility to approximate the angle x.
(Enter your answers as a comma-separated list. Round each answer to four decimal places.)
tan^2 x + 5 tan x + 3 = 0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Introduce new variable u = tan(x).
Then your equation becomes

u%5E2+%2B+5u+%2B+3 = 0.

Solve this quadratic equation by quadratic formula. You will get

u%5B1%2C2%5D = %28-5+%2B-+sqrt%2825-4%2A3%29%29%2F2 = %28-5+%2B-+sqrt%2813%29%29%2F2.

u%5B1%5D = %28-5%2Bsqrt%2813%29%29%2F2  --->  tan(x) = %28-5%2Bsqrt%2813%29%29%2F2  --->  x = arctan%28%28-5%2Bsqrt%2813%29%29%2F2%29  --->  apply your calculator.

u%5B2%5D = %28-5-sqrt%2813%29%29%2F2  --->  tan(x) = %28-5-sqrt%2813%29%29%2F2  --->  x = arctan%28%28-5-sqrt%2813%29%29%2F2%29%29  --->  apply your calculator.