Find a monic polynomial f(x) of least degree over C

Chris Cruz

Chris Cruz

Answered question


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

Step 1
The zeros of the polynomial 3-i, i and 2
Step 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 a1,a2,a3,a4,a5 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 (x3+i)(x3i)=x26x+10
Therefore, the required monic polynomial is f(x)=x58x4+23x328x2+22x20

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