Algebra · Polynomials · Linear inequalities · Parameters
Find all real numbers \(r\) for which there exists exactly one real number \(a\) such that the polynomial
\[ p(x) = (x + a)\left(x^2 + rx + 1\right) \]
has all of its coefficients nonnegative.
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Serbian Regional Competition (Okruzno takmicenje) 2024, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source