Q56 / 160 · TS EAMCET 2005 · Mathematics
The roots of the equation $x^3-3 x-2=0$ are
- Correct answerA$-1,-1,2$
- B$-1,1,-2$
- C$-1,2,-3$
- D$-1,-1,-2$
Solution
Given equation is
$x^3-3 x-2=0$
Now, put $x=-1$, we get
$\begin{aligned}
(-1)^3-3(-1)-2 & =0 \\
\Rightarrow \quad 0 & =0
\end{aligned}$
Given equation can be written as
$\begin{aligned}
& \therefore \quad(x+1)\left(x^2-x-2\right)=0 \\
& \Rightarrow \quad(x+1)(x+1)(x-2)=0 \\
& \Rightarrow \quad x=-1,-1,2 \\
&
\end{aligned}$
Hence, the correct answer is option: 'A'.