The equation $x^4-x^3-6 x^2+4 x+8=0$ has two equal roots. If $\alpha, \beta$ are the other two roots of this equation then $\alpha^2+\beta^2=$

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Aicharya · Accepted Answer

$x^4-x^3-6 x^2+4 x+8=0$ By Hit and trial $x=2$ is a root of the equation $\Rightarrow(x-2)\left(x^3+x^2-4 x-4\right)=0$
Again $x=2$ is a root of the equation $\begin{aligned} & \Rightarrow(x-2)^2\left(x^2+3 x+2\right)=0 \\ & \Rightarrow(x-2)^2(x-1)(x+2)=0 \Rightarrow x=2,2,-2,1 \\ & \Rightarrow \alpha=-2, \beta=1 \Rightarrow \alpha^2+\beta^2=5 \end{aligned}$

The equation $x^4-x^3-6 x^2+4 x+8=0$ has two equal roots. If $\alpha, \beta$ are the other two roots of this…

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