The roots of the polynomial 

\[
f(x) = x^4 - 2x^3 + 2x^2 + 3x - 4
\] 

are:

1. \( 1.0755 + 1.5228i \) 
2. \( 1.0755 - 1.5228i \)
3. \( -1.1509 \)
4. \( 1 \)

These roots include both complex and real values, as found directly using numerical methods. 

Would you like more details on the method used, or do you have any further questions? Here are some related questions that might interest you:

1. How does Bairstow's method handle complex roots?
2. What are some alternative methods for finding polynomial roots?
3. Can we refine the accuracy of the roots further?
4. How to analyze the stability of numerical methods for root-finding?
5. What are the conditions under which Bairstow's method might fail?

**Tip:** When dealing with high-degree polynomials or numerical instabilities, using robust library functions like `numpy.roots` can save time and avoid complex calculations.

Discover how to find roots of the polynomial x^4 - 2x^3 + 2x^2 + 3x - 4, which includes both complex and real values. This problem uses numerical methods and explores concepts like polynomial equations, complex numbers, and root-finding techniques like Bairstow's method. Suitable for advanced high school and college students.

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