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

tebollahb

tebollahb

Answered question

2022-01-14

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.
-3i, 4

Answer & Explanation

Esta Hurtado

Esta Hurtado

Beginner2022-01-15Added 39 answers

Step 1
Given,
Zeros, −3i,4
it has three zeros ±3i,4
these zeros are factor of the equation
g(x)=(x-3i)(x+3i)(x-4)
now solve this equation
(x2+9)(x4)=0
x34x2+9x36=0
so it is a cubic polynomial
Step 2
so polynomial is x34x2+9x36=0

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