Step-by-step explanation:
The given cubic polynomial:
k(x) = [tex]x^3[/tex] + 2[tex]x^2[/tex] - x -2
To find, the all roots are [tex]x^3[/tex] + 2[tex]x^2[/tex] - x -2 = ?
∴ k(x) = [tex]x^3[/tex] + 2[tex]x^2[/tex] - x -2
⇒ [tex]x^3[/tex] + 2[tex]x^2[/tex] - x -2 = 0
⇒ [tex]x^2[/tex](x + 2) - 1(x + 2) = 0
⇒ ([tex]x^2[/tex] - 1)(x + 2) = 0
⇒ [tex]x^2[/tex] - 1 = 0 and x + 2 = 0
⇒ [tex]x^2[/tex] - 1 = 0
⇒ [tex]x^2[/tex] = 1
⇒ x = ± 1 = 1, - 1
or, x + 2 = 0
⇒ x = - 2
Thus, the all roots are equation are 1, - 1 and - 2.
