If the zeros of the polynomial x^{3} – 3x^{2} + x + 1 are (a ‒ b), a and (a + b), find the values of a and b

It is given in the question that the roots of the given polynomial are (a – b), a and (a + b)

Now by comparing the given polynomial with Ax^{3} + Bx^{2} + Cx + D, we get:

A = 1, B = - 3, C = 1 and D = 1

Now,

(a – b) + a + (a + b) =

3a = -

a = 1

Also, we have:

(a – b) × a × (a + b) =

a (a^{2} – b^{2}) =

1 (1^{2} – b^{2}) = - 1

1 – b^{2} = - 1

b^{2} = 2

b =

Hence, a = 1 and b =

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