Find a monic polynomial f(x) of least degree over C that has the given numbers...
Find a monic polynomial f(x) of least degree over C that has the given numbers as zeros, and a monic polynomial g(x) of least degree with real coefficients that has the given numbers as zeros.
3- i, i, and 2
Answer & Explanation
Beginner2021-12-12Added 39 answers
The zeros of the polynomial 3-i, i and 2
The complex roots occur in pair, so conjugate of 3-i and i also be the zeros of the same polynomial
So, the polynomial has zeros: 3-i, 3+i, i , -i and 2
If are the zeros of the polynomial then the polynomial in factored form is written as:
Where a is the leading coefficient since the given polynomial is monic so the leading coefficient is 1.
Simplifying we get
Therefore, the required monic polynomial is
Plainmath is a platform aimed to help users to understand how to solve math problems by providing accumulated knowledge on different topics and accessible examples. Plainmath.net is owned and operated by RADIOPLUS EXPERTS LTD.