Show, by considering its minimum, that f (x) = x2 2x + 3 takes on only positive values

Chapter 4, Problem 92

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Show, by considering its minimum, that f (x) = x2 2x + 3 takes on only positive values. More generally, find the conditions on r and s under which the quadratic function f (x) = x2 + rx + s takes on only positive values. Give examples of r and s for which f takes on both positive and negative values.

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