Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

For two real roots (so $k\ne -1$ ), the discriminant is $4\left(5-k^2\right)\ge 0$. Their sum is $4/(1+k)$ and product $(k-1)/(1+k)$; hence the tangent of their sum is 2 . At $k=2,\tan x=1,1/3$, and at $k=1,\tan x=0,2$. At $k=-1$ there is only one linear root, so the premise of two roots excludes it.