If the zeroes of the polynomialx3 - 3x2 + x + 1 are a - b, a , a + b, finda and b .

p(x) = x³ -3x²+x+1

Zeroes are a − b, a + a + b Comparing the given polynomial with px³+qx²+rx+1, we obtain p = 1, q = −3, r = 1, t = 1

Sum of zeros = a – b + a + a + b

^-q/ _p = 3a

–^(-3)/₁ = 3a

3 = 3a

a = 1

The zeroes are 1-b, 1, 1+b

Multiplication of zeroes = 1(1-b)(1+b)

^-t/_p = 1 – b²

^-1/₁= 1 – b²

1 – b² = -1

1 + 1 = b²

b = ±√2