SOLUTION: Find all solutions of the equation in the interval [0, 2π). 6 cos ^2 x + 3 cos x − 3 = 0

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Question 1078894: Find all solutions of the equation in the interval [0, 2π).
6 cos ^2 x + 3 cos x − 3 = 0
Answer by ikleyn(52908)   (Show Source): You can put this solution on YOUR website!
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Find all solutions of the equation in the interval [0, 2π).
6 cos ^2 x + 3 cos x − 3 = 0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

 =     --->  cancel the factor "3" in both sides. You will get

 =    --->  Factor both sides. You will get


(2cos(x)-1)*(cos(x) +1) = 0.


The last equation deploys in two independent equations


1.  2cos(x) - 1 = 0  <---->  cos(x) = .  This equation has two solutions x =  and/or  x = .


2.  cos(x) +1 = 0  <---->  cos(x) = -1.   This equation has the root x = .


Answer.  In the given interval, the original equation has three solutions  x = ,  x =  and x = .


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