tebollahb

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

Expert

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
$\left({x}^{2}+9\right)\left(x-4\right)=0$
${x}^{3}-4{x}^{2}+9x-36=0$
so it is a cubic polynomial
Step 2
so polynomial is ${x}^{3}-4{x}^{2}+9x-36=0$

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