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Two real roots of magnitude less than 1

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October 28, 2010
algebrapolynomialVietaalgebra unsolved

Problem Statement

Consider a polynomial P(x)=ax2+bx+cP(x) = ax^2 + bx + c with a>0a > 0 that has two real roots x1,x2x_1, x_2. Prove that the absolute values of both roots are less than or equal to 11 if and only if a+b+c≥0,a−b+c≥0a + b + c \ge 0, a -b + c \ge 0, and a−c≥0a - c \ge 0.
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