Find the transformed equation whose roots are the negatives of the roots of $x^{4} + 5 x^{3} + 11 x + 3 = 0$ .

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Solution

To get transformed equation whose roots are negative of above equation
replace $x$ by $- x$
$\Rightarrow (- x)^{4} + 5 (- x)^{3} + 11 (- x) + 3 = 0$
$\Rightarrow x^{4} - 5 x^{3} - 11 x + 3 = 0$

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