SOLUTION: Solve over the interval [0, 2pi) : 3cot^2x-3cotx-1=0 I used the quadratic formula and got x=0.67, 1.83 and 4.97

Algebra ->  Trigonometry-basics -> SOLUTION: Solve over the interval [0, 2pi) : 3cot^2x-3cotx-1=0 I used the quadratic formula and got x=0.67, 1.83 and 4.97      Log On


   

Question 1116546: Solve over the interval [0, 2pi) : 3cot^2x-3cotx-1=0
I used the quadratic formula and got x=0.67, 1.83 and 4.97
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve over the interval [0, 2pi) : 3cot^2x-3cotx-1=0
---------
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-3x%2B-1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-3%29%5E2-4%2A3%2A-1=21.

Discriminant d=21 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+21+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+21+%29%29%2F2%5C3+=+1.26376261582597
x%5B2%5D+=+%28-%28-3%29-sqrt%28+21+%29%29%2F2%5C3+=+-0.263762615825973

Quadratic expression 3x%5E2%2B-3x%2B-1 can be factored:
3x%5E2%2B-3x%2B-1+=+%28x-1.26376261582597%29%2A%28x--0.263762615825973%29
Again, the answer is: 1.26376261582597, -0.263762615825973. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-3%2Ax%2B-1+%29

===================
tan(x) = 1/cot(x)
tan(x) = 0.79128786
x = 0.90139, 4.04298
-------------
tan(x) = -3.791288
x = 4.9703, 1.82869