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If $\alpha, \beta, \gamma$ and $\delta$ are the roots of the equation $x^4+3 x^3-6 x^2+2 x-4=0$, then find the equation having roots $\frac{1}{\alpha}, \frac{1}{\beta}, \frac{1}{\gamma}$ and $\frac{1}{\delta}$
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The correct answer is:
$4 x^4-2 x^3+6 x^2-3 x-1=0$
It is given that the equation $x^4+3 x^3-6 x^2+2 x-4=0$ having roots $\alpha, \beta, \gamma$ and $\delta$, then equation having roots $\frac{1}{\alpha}, \frac{1}{\beta}, \frac{1}{\gamma}$ and $\frac{1}{\delta}$ can be obtained by replacing $x$ by $\frac{1}{x}$ in given equation, so required equation is
$$
4 x^4-2 x^3+6 x^2-3 x-1=0
$$
$$
4 x^4-2 x^3+6 x^2-3 x-1=0
$$
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