Quintic Pi Polynomial

Calculus Level 2

3x5=1x4+4x3+1x2+5x+9 \large \color{#D61F06}{3}x^{5} \color{#3D99F6}{=} \color{#D61F06}{1}x^{4} + \color{#D61F06}{4}x^{3} + \color{#D61F06}{1}x^{2} + \color{#D61F06}{5}x + \color{#D61F06}{9}

The above polynomial has exactly one real root α \alpha . Find 1000×α \lfloor 1000 \times \alpha \rfloor .

Notation: x \lfloor x \rfloor denotes the greatest integer smaller than or equal to xx. This is known as the greatest integer function.

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