1

Part of 2021 Taiwan APMO Preliminary First Round

Problems(1)

Min of (|b|+|c|)/a

Source: 2021 Taiwan APMO Preliminary First Round

Let the three roots of

x^3+ax+1=0

\alpha,\beta,\gamma

a

is a positive real number. Let the three roots of

x^3+bx^2+cx-1=0

\frac{\alpha}{\beta},\frac{\beta}{\gamma},\frac{\gamma}{\alpha}

. Find the minimum value of

\dfrac{|b|+|c|}{a}