 # Find a monic polynomial f(x) of least degree over C Gregory Emery 2022-01-16 Answered
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.
2i, 3
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Step 1: Introduction
Monic Polynomial: Mono stands for Single Therefore it is a type of polynomial having single variable or single constraints used in the function. The degree of the polynomial or the highest power of the given polynomial is 1.
Step 2: To 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.
Step 3: Solution to the question
Both 2i and 3 are the zeroes of the functions, therefore,
We have,
f(x)=(x-2i)(x-3)
=x(x-3)-2i(x-3)
$={x}^{2}-3x-2ix+6i$
$={x}^{2}-\left(3x+2i\right)x+6i$
g(x)=(x-2i)(x+2i)(x-3)
$=\left({x}^{2}-{\left(2i\right)}^{2}\right)\left(x-3\right)$
$=\left({x}^{2}+4\right)\left(x+3\right)$
$={x}^{3}+3{x}^{2}+4x+12$
###### Not exactly what you’re looking for? Medicim6
To find a monic polynomial f(x) of least degree over C that has the given numbers as zeroes and a monic polynomials g(x) of least degree with real coefficient that has given numbers as zeroes.
2i, 3
f(x)=(x-2i)(x-3)
$={x}^{2}-\left(3+2i\right)x+6i$
g(x)=(x-2i)(x+2i)(x-3)
$=\left({x}^{2}+4\right)\left(x-3\right)$
$={x}^{3}-3{x}^{2}+4x-12$.