The Complexity's Simplicity

Algebra Level 3

Consider the equation \(ax^{2} + bx + c = 0\), in which a, b and c are real numbers and \(a > 0\). Suppose that this equation has two real roots, r and s, where \(0 < r < 1\) and \(0 < s < 1\). Is it true to say that \(b + c < 0\)?

This problem was not created by me. It is from the Brazilian Maths Olympiads (OBM), of the year 2013.
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