The algebraic equation of degree 4 whose roots are the translates of the roots of the equation $x^4+5 x^3+6…

The algebraic equation of degree 4 whose roots are the translates of the roots of the equation $x^4+5 x^3+6 x^2+7 x+9$ $=0$ by -1 is
  1. $x^4+x^3-3 x^2+6 x+4=0$
  2. $x^4+9 x^3+27 x^2+38 x+28=0$
  3. $x^4+5 x^3+6 x^2+7 x+9=0$
  4. $x^4-5 x^3+6 x^2-7 x+9=0$

Solution

$\begin{aligned} & \text { Replacing ' } x \text { ' by }(x+1) \text { we get, } \\ & =(x+1)^4+5(x+1)^3+6(x+1)^2+3(x+1)+9 \\ & \Rightarrow x^4+9 x^3+27 x^2+38 x+28=0\end{aligned}$

Asked in: AP EAMCET 2024 (21 May Shift 1)

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