If the zeros of the polynomial f(x) = x3 – 3x2 + x + 1 are (a –

1.	If the zeros of the polynomial f(x) = x3 – 3x2 + x + 1 are (a – b), a and (a + b), find a and b.
Answer» 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

If the zeros of the polynomial f(x) = x3 – 3x2 + x + 1 are (a – b), a and (a + b), find a and b.

Answer»

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