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.
by
Calvin Lin