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

1.	If the zeroes of the polynomial f(x) = x3 – 3x2 + x + 1 are (a – b), a and (a + b), find the values of a and b.
Answer» By using the relationship between the zeroes of he quadratic polynomial. We have, Sum of zeroes = \(\frac{-(coefficient\,of\,x^2)}{coefficient\,of\,x^3}\) ∴ a – b + a + a + b = \(\frac{-(-3)}1\) ⇒ 3a = 3 ⇒ a = 1 Now, Product of zeroes = \(\frac{-(constant\,term)}{coefficient\,of\,x^3}\) ∴ (a – b) (a) (a + b) = \(\frac{-1}1\) ⇒ (1 – b) (1) (1 + b) = –1 [∵a =1] ⇒ 1 – b² = –1 ⇒ b² = 2 ⇒ b = ±√2

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

Answer»

By using the relationship between the zeroes of he quadratic polynomial.

We have,

Sum of zeroes = \(\frac{-(coefficient\,of\,x^2)}{coefficient\,of\,x^3}\)

∴ a – b + a + a + b = \(\frac{-(-3)}1\)

⇒ 3a = 3

⇒ a = 1

Now,

Product of zeroes = \(\frac{-(constant\,term)}{coefficient\,of\,x^3}\)

∴ (a – b) (a) (a + b) = \(\frac{-1}1\)

⇒ (1 – b) (1) (1 + b) = –1 [∵a =1]

⇒ 1 – b² = –1

⇒ b² = 2

⇒ b = ±√2