Let f: R - \0 → (-∞, 1) be a polynomial of degree 2, satisfying f(x) f(1/x) = f(x) + f(1/x). If f(K) = -2K, then the sum of squares of all possible values of K is:

Sets, Relations and Functions: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q88

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumSets, Relations and Functions168× since 2002

Let

f: \mathbb{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(K) = -2K

, then the sum of squares of all possible values of

K

is:

JEE Main 2025 · January, Unspecified (session-level dataset) · Q88

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumSets, Relations and Functions168× since 2002

Let

f: \mathbb{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(K) = -2K

, then the sum of squares of all possible values of

K

is: