SOLUTION: To the nearest ten minutes, find all values of x in the interval 0 less than or equal to x less than or equal to 360 that satisfy {{{ 3tan^2(x)+5tan(x)=2 }}}

Question 754360: To the nearest ten minutes, find all values of x in the interval 0 less than or equal to x less than or equal to 360 that satisfy
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
To the nearest ten minutes, find all values of x in the interval 0 less than or equal to x less than or equal to 360 that satisfy
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Sub u for tan(x)

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=49 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.333333333333333, -2. Here's your graph:

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tan(x) = 1/3
x = 18.435, 198.435 degs
tan(x) = -2
x = 116.565, 296.565 degs
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