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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Expert Answer

jgardner33v4
Answered 2022-01-17 Author has 35 answers
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)
=x23x2ix+6i
=x2(3x+2i)x+6i
g(x)=(x-2i)(x+2i)(x-3)
=(x2(2i)2)(x3)
=(x2+4)(x+3)
=x3+3x2+4x+12
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Medicim6
Answered 2022-01-18 Author has 33 answers
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)
=x2(3+2i)x+6i
g(x)=(x-2i)(x+2i)(x-3)
=(x2+4)(x3)
=x33x2+4x12.
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