Given: Zeros of the polynomial x3 – 3x2 + 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 = -(coefficient of x)/(coefficient of x2) = -1
a – b + a + a + b = -1
3a = 3
a = 1
Product of zeros = (constant term)/(coefficient of x2) = -1
(a – b) (a) (a + b) = -1
(1 – b) (1) (1 + b) = – 1
1 – b2 = – 1
b = ±√2