# Does perfect square imply perfect square polynomial?

Algebra Level 2

True or false:

Consider a quadratic expression $$f(x) = x^2 + bx + c$$, where $$b$$ and $$c$$ are rational numbers. If for all rational numbers $$r$$, $$f(r)$$ is the square of a rational number, then $$f(x)$$ must be the square of a linear polynomial.

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