Answer :

x^{3} – 2x^{2} – x + 2 = 0

p(x) = x^{3} – 2x^{2} – x + 2 = 0

p(-1) = (-1)^{3} – 2(-1)^{2} - (-1) + 2

= -1 – 2 × 1 + 1 + 2

= -1 – 2 + 1 + 2

= -3 + 3 = 0

∴ x = -1 is a root of x^{3} – 2x^{2} – x + 2 = 0

p(x) = x^{3} – 2x^{2} – x + 2 = 0

p(2) = (2)^{3} – 2(2)^{2} – (2) + 2

= 8 – 2 × 4 – 2 + 2

= 8 – 8 – 2 + 2

= 10 – 10 = 0

∴ x = 2 is a root of x^{3} – 2x^{2} – x + 2 = 0.

p(x) = x^{3} – 2x^{2} – x + 2 = 0

p(3) = (3)^{3} – 2(3)^{2} – (3) + 2

= 27 – 2 × 9 – 3 + 2

= 27 – 18 – 3 + 2

= 29 – 21 = 8 ≠ 0

∴ x = 3 is not a root of x^{3} – 2x^{2} – x + 2 = 0.

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