SOLUTION: The smallest positive number for which 4cos^2(x)-9cos(x)+2 = 0 Hint: Solve the quadratic equation for cos x and then solve for x.

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Question 544853: The smallest positive number for which
4cos^2(x)-9cos(x)+2 = 0
Hint: Solve the quadratic equation for cos x and then solve for x.
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
Set y = cos(x)


4y%5E2+-9y+%2B2+=0
Factor.


(4y - 1)(y - 2)=0
4y=1 ---> y=.25
y=2


This means:
cos(x) = 2 which is not possible because cosine fluctuates between -1 and 1.


cos(x)=.25
use arccos(.25)=x to find the unknown angle. It's about 75.5 degrees.

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