Express f (x) as a product of linear and quadratic polynomials with real coefficients that are irreducible over R. -1,0,3+i. degree 4
slaggingV 2021-09-03Answered
A polynomial f (x) with real coefficients and leading coefficient 1 has the given zero(s) and degree. Express f (x) as a product of linear and quadratic polynomials with real coefficients that are irreducible over R.
degree 4
Given Roots of the polynomial of degree 4 is -1, 0, 3+i
To find the polynomial f (x) with real coefficients and leading coefficient 1 has the given zero(s) and degree. Also, to Express f (x) as a product of linear and quadratic polynomials with real coefficients that are irreducible over R.
Definition Used We know if a polynomial having a complex root then its complex conjugate will also be the root of the given polynomial.
Formation of the polynomial f(x)
Since by the definition if 3+i is one root then 3-i will also be the root of the given polynomial
In this way, we have a total number of 4 zeroes i.e.
-1,0,3+i and 3-i
Then the polynomial f(x) is