If x^{3} + x^{2} ‒ ax + b is divisible by (x^{2} ‒ x), write the values of a and b.

Firstly, equating x^{2} – x to 0 to find the zeros we get:

x (x – 1) = 0

x = 0 or x – 1 = 0

x = 0 or x = 1

As x^{3} + x^{2} – ax + b is divisible by x^{2} – x

∴ The zeros o x^{2} – x will satisfy x^{3} + x^{2} – ax + b

Hence, (0)^{3} + 0^{2} – a (0) + b = 0

b = 0

Also,

(1)^{3} + 1^{2} – a (1) + 0 = 0

∴ a = 2

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