If the zeros of the polynomial f(x) = x^{3} – 3x^{2} + x + 1 are (a – b), a and (A + b), find the a and b.

It is given in the question that,

Zeros of the polynomial x^{3} – 3x^{2} + x + 1 are (a – b), a and (a + b)

Now by using the relationship between the zeros of the quadratic polynomial we have:

Sum of zeros =

a – b + a + a + b =

3a = 3

a =

Now, we have product of zeros =

(a – b) (a) (a + b) =

(1 – b) (1) (1 + b) = - 1

1 – b^{2} = - 1

b^{2} = 2

∴ b =

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