Find a polynomial equation of minimum degree with rational coefficient

1.	Find a polynomial equation of minimum degree with rational coefficients, having 2 + √3i as a root.
Answer» Given roots is (2 + √3i) The other root is (2 – √3i), since the imaginary roots with real co-efficient occur as conjugate pairs. x² – x(S.O.R) + P.O.R = 0 ⇒ x² – x(4) + (4 + 3) = 0 ⇒ x² – 4x + 7 = 0

Find a polynomial equation of minimum degree with rational coefficients, having 2 + √3i as a root.

Answer»

Given roots is (2 + √3i)

The other root is (2 – √3i), since the imaginary roots with real co-efficient occur as conjugate pairs.

x² – x(S.O.R) + P.O.R = 0

⇒ x² – x(4) + (4 + 3) = 0

⇒ x² – 4x + 7 = 0