Problem

Find the complex zeros of the following polynomial functio \[ f(x)=x^{3}-9 x^{2}+31 x-39 \]

Solution

Step 1 :We are given the polynomial function \(f(x)=x^{3}-9 x^{2}+31 x-39\).

Step 2 :We need to find the complex zeros of this polynomial function.

Step 3 :We use the numpy.roots() function to calculate the roots of the polynomial with coefficients given in a list. The roots may be real or complex numbers.

Step 4 :The coefficients of the polynomial are [1, -9, 31, -39].

Step 5 :The roots of the polynomial are 3+2j, 3-2j, and 3.

Step 6 :These are the complex zeros of the polynomial function.

Step 7 :Final Answer: The complex zeros of the polynomial function are \(\boxed{3+2j}\), \(\boxed{3-2j}\), and \(\boxed{3}\).

From Solvely APP
Source: https://solvelyapp.com/problems/SrCVOX60GE/

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