A subset of the real numbers SCR is defined by the statement that x E S whenever x is a real root of a monic quadratic polynomial with integer coefficients, or in other words x satisfies an equation of the form x² +₁x + ₁ = 0 for some integers Co, C₁ € Z. (a) Show that 0 € S and 1 € S. (b) Show that ZCS. (c) Show that Z ‡ S, in other words Z is a proper subset of S.

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