Question

Given f(x)= x3 - 2x2 - X + 2,the roots of f(x) areDONE1, -2, -1, 21-1, 1, 21-1, 1, -2-1,1, -2,01-1, 1, 2,0

Answer 1

Given data:

$f(x)=x^3-2x^2-x+2$

To find the roots ,

$x^3-2x^2-x+2=0^{}$

Now, by using long division method

$\frac{x^3-2x-x+2}{x-1}=x^2-x-2$

Solving further,

$\begin{gathered} x^2-x-2=0 \\ x^2-2x+x-2=0 \\ x(x-2)+1(x-2)=0_{} \\ (x+1)(x-2)=0 \end{gathered}$$\begin{gathered} x+1=0 \\ x-2=0 \end{gathered}$

Thus, the roots of the polynomial are 2 , -1 , 1

The correct option is (2)