Let $r_1,$ $r_2,$ $r_3,$ and $r_4$ be the roots of
\[x^4 - 2x^3 - 5x^2 + 4x - 1 = 0.\]Find the monic polynomial, in $x,$ whose roots are $\frac{1}{r_1},$ $\frac{1}{r_2},$ $\frac{1}{r_3},$ and $\frac{1}{r_4}.$
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<|im_start|>user
Let $r_1,$ $r_2,$ $r_3,$ and $r_4$ be the roots of
\[x^4 - 2x^3 - 5x^2 + 4x - 1 = 0.\]Find the monic polynomial, in $x,$ whose roots are $\frac{1}{r_1},$ $\frac{1}{r_2},$ $\frac{1}{r_3},$ and $\frac{1}{r_4}.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
x^4 - 4x^3 + 5x^2 + 2x - 1
Let $r_1,$ $r_2,$ $r_3,$ and $r_4$ be the roots of
\[x^4 - 2x^3 - 5x^2 + 4x - 1 = 0.\]Find the monic polynomial, in $x,$ whose roots are $\frac{1}{r_1},$ $\frac{1}{r_2},$ $\frac{1}{r_3},$ and $\frac{1}{r_4}.$
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