Find a polynomial equation of minimum degree with rational co-efficien

1.	Find a polynomial equation of minimum degree with rational co-efficients having 1 – i as a root.
Answer» Given root is 1 – i The other root is 1 + i Sum of the roots: 1 – i + 1 + i = 2 product of the roots: (1 – i) (1 + i) = (1)² + (1)² ⇒ 1 + 1 = 2 ∴ The required polynomial equation of minimum degree with rational coefficients is x² – x (S.R.) + (P.R.) = 0 x² – 2x + 2 = 0

Find a polynomial equation of minimum degree with rational co-efficients having 1 – i as a root.

Answer»

Given root is 1 – i

The other root is 1 + i

Sum of the roots: 1 – i + 1 + i = 2

product of the roots: (1 – i) (1 + i) = (1)² + (1)²

⇒ 1 + 1 = 2

∴ The required polynomial equation of minimum degree with rational coefficients is

x² – x (S.R.) + (P.R.) = 0

x² – 2x + 2 = 0