Let a be a nonzero real number. Evaluate lim, f(r) and lim, - f(z), where f(r) = ar" - 3r + 6z - 722 + 10. State a result that guarantees the existence of a real root of the polynomial f(r) given the limits above. What would go wrong in this argument if we replace f(x) with a polynomial of an even degree?

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