f(x) is a polynomial function, $f : R \to R,$ such that $f (2 x) = f^{'} (x) f^{''} (x) .$ Equation f(x) = x has (A) three real and positive roots (B) three real and negative roots (C) one real root (D) three real roots such that sum of roots is zero

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f(x) is a polynomial function,

f : R \to R,

such that

f (2 x) = f^{'} (x) f^{''} (x) .

Equation f(x) = x has (A) three real and positive roots (B) three real and negative roots (C) one real root (D) three real roots such that sum of roots is zero

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f(x) is a polynomial function,

f : R \to R,

such that

f (2 x) = f^{'} (x) f^{''} (x) .

Equation f(x) = x has (A) three real and positive roots (B) three real and negative roots (C) one real root (D) three real roots such that sum of roots is zero

f(x) is a polynomial function, $f : R \to R,$ such that $f (2 x) = f^{'} (x) f^{''} (x) .$ Equation f(x) = x has (A) three real and positive roots (B) three real and negative roots (C) one real root (D) three real roots such that sum of roots is zero

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f(x) is a polynomial function, f:R→R, such that f(2x)=f′(x)f′′(x). Equation f(x) = x has (A) three real and positive roots (B) three real and negative roots (C) one real root (D) three real roots such that sum of roots is zero

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f(x) is a polynomial function, $f : R \to R,$ such that $f (2 x) = f^{'} (x) f^{''} (x) .$ Equation f(x) = x has (A) three real and positive roots (B) three real and negative roots (C) one real root (D) three real roots such that sum of roots is zero