If the equation $x^4+7 x^3+18 x^2+20 x+8=0$ has a repeated root, then that repeated root is

If the equation $x^4+7 x^3+18 x^2+20 x+8=0$ has a repeated root, then that repeated root is
  1. $-2$
  2. $-1$
  3. $-3$
  4. $-4$

Solution

Given equation is $x^4+7 x^3+18 x^2+20 x+8=0$ $\begin{aligned} & \Rightarrow x^4+2 x^3+5 x^3+10 x^2+8 x^2+16 x+4 x+8=0 \\ & \Rightarrow(x+2)\left(x^3+5 x^2+8 x+4\right)=0 \\ & \Rightarrow(x+2)\left(x^3+2 x^2+3 x^2+6 x+2 x+4\right)=0 \\ & \Rightarrow(x+2)(x+2)\left(x^2+3 x+2\right)=0 \end{aligned}$ so repeated roots $=-2$

Asked in: AP EAMCET 2023 (16 May Shift 2)

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