Thanks CPhill,
CPhill and I have both interpreted your question to mean
$$y=tan^2x+tanx$$
If x=0 then y=0 because tan0=0
If y=0 then
$$\\tanx(tanx+1)=0\\\\
tanx=0\;\;or\;\;tanx+1=0\\\\
sinx=0\;\;or\;\;tanx=-1\\\\
x=n\pi\pm \frac{\pi}{2}\;\;\;or\;\;\;x=n\pi\pm \frac{3\pi}{4}\qquad n\in Z$$
My answer is the same as CPhill"s
Here's a graph.........https://www.desmos.com/calculator/wpfchryj3k
This function intersects the x axis at -45° + k*180° and at 0° + k*180° {where k is an integer}
It only intersects the y axis at the origin....!!!!
Thanks CPhill,
CPhill and I have both interpreted your question to mean
$$y=tan^2x+tanx$$
If x=0 then y=0 because tan0=0
If y=0 then
$$\\tanx(tanx+1)=0\\\\
tanx=0\;\;or\;\;tanx+1=0\\\\
sinx=0\;\;or\;\;tanx=-1\\\\
x=n\pi\pm \frac{\pi}{2}\;\;\;or\;\;\;x=n\pi\pm \frac{3\pi}{4}\qquad n\in Z$$
My answer is the same as CPhill"s