If the equation having the roots as the values obtained oy diminishing each root of the equation $x^3-3…
If the equation having the roots as the values obtained oy diminishing each root of the equation $x^3-3 x^2+2 x-1=0$ by $\mathrm{K}$ is $\mathrm{x}^3-\mathrm{x}-1=0$, then $\mathrm{K}=$
$2$
$-1$
$1$
$-2$
Solution
Let $\alpha, \beta, \gamma$ be the root of $x^3-3 x^2+2 x-1=0$
Then, $\alpha+\beta+\gamma=3$
Roots of $\mathrm{x}^3-\mathrm{x}-1=0$ is : $\alpha-\mathrm{k}, \beta-\mathrm{k}, \gamma-\mathrm{k}$
Then, $(\alpha-k)+(\beta-\mathrm{k})+(\gamma-\mathrm{k})=0$
$\begin{aligned} & \Rightarrow \alpha+\beta+\gamma-3 \mathrm{k}=0 \\ & \Rightarrow 3-3 \mathrm{k}=0 \Rightarrow \mathrm{k}=1\end{aligned}$