Let \(f: \mathbf{R}-\{0\} \rightarrow(-\infty, 1)\) be a polynomial of degree 2 , satisfying \(f(x) f\left(\frac{1}{x}\r…

Let \(f: \mathbf{R}-\{0\} \rightarrow(-\infty, 1)\) be a polynomial of degree 2 , satisfying \(f(x) f\left(\frac{1}{x}\right)=f(x)+f\left(\frac{1}{x}\right)\). If \(f(\mathrm{~K})=-2 \mathrm{~K}\), then the sum of squares of all possible values of K is :

[JEE Main 2025, 28 Jan (Shift 2)]