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

Question

Philoid · Accepted Answer

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 Ax³ + Bx² + 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 (a² – b²) =

1 (1² – b²) = - 1

1 – b² = - 1

b² = 2

b =

Hence, a = 1 and b =