Answer :

x^{3} – 2x^{2} – 5x + 6 = 0

let p(x) = x^{3} – 2x^{2} – 5x + 6

p(1) = (1)^{3} – 2(1)^{2} – 5(1) + 6

= 1 – 2 × 1 – 5 + 6

= 1 – 2 – 5 + 6

= 7 – 7 = 0

∴ x = 1 is a root of x^{3} – 2x^{2} – 5x + 6 = 0.

p(x) = x^{3} – 2x^{2} – 5x + 6

p(-2) = (-2)^{3} – 2(-2)^{2} – 5(-2) + 6

= -8 – 2 × 4 – 5 × 2 + 6

= -8 – 8 + 10 + 6

= -16 + 16 = 0

∴ x = -2 is a root of x^{3} – 2x^{2} – 5x + 6 = 0.

p(x) = x^{3} – 2x^{2} – 5x + 6 = 0

p(3) = (3)^{3} – 2(3)^{2} – 5(3) + 6

= 27 – 2 × 9 – 5 × 3 + 6

= 27 – 18 – 15 + 6

= 33 – 33 = 0

∴ x = 3 is a root of x^{3} – 2x^{2} – 5x + 6 = 0.

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