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

a = 2, b = 0

Given,

A polynomial f(x) = x^{3} + x^{2} – ax + b

Which is divisible by x^{2} – x

Now,

x^{2} – x = (x – 1) = (x – 0)(x – 1)

(x – 0) and (x – 1) are factors of polynomial f(x)

⇒ f(0) = 0

⇒ 0^{3} + 0 – a × 0 + b = 0

⇒ b = 0

And f(1)

1^{3} + 1 – a × 1 + b = 0

⇒ 2 – a = 0

⇒ a = 2

∴ a = 2 and b = 0

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