Question

If the zeroes of the polynomial x^3 – 3x^2 + x + 1 are a – b, a, a + b, find a and b.

Answer 1

p(x) = x³ - 3x² + x + 1

Zeroes are a − b, a + a + b

Comparing the given polynomial with px³ + qx² + rx + t , we obtain

p = 1, q = −3, r = 1, t = 1

The zeroes are 1-b, 1, 1+b .

Hence, a = 1 and b = √2 or -√2.