a hard polynomial problem – math.stackexchange.com

Let $f(x) = x^4 + 14x^3 + 52x^2 + 56x + 16.$ Let $z_1, z_2, z_3, z_4$ be the four roots of $f$. Find the smallest possible value of $|z_az_b + z_cz_d|$ where ${a, b, c, d} = {1, 2, 3, 4}.$ So I ...

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