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1. Find the number of real roots and imaginary roots:
2. Find all zeros:
3. Find all roots:
f(x)=x^3-7x^2-17x-15; 2 + i
4. Find all roots:
f(x)=x^4-6x^3+12x^2+6x-13; 3 + 2i
The 5th problem is attached.
Please answer the questions above and show the work done. Thank you!© BrainMass Inc. brainmass.com May 24, 2023, 1:16 pm ad1c9bdddf
1.Find the number of real roots and imaginary roots:
In order to find all real roots, we must count the number of times the sign changes in the equation for f(x). Thus, there are two sign changes, from +10 to -34, and -8 to +3. Thus, there are two positive real roots.
In order to find the number of negative real roots, we need to count the sign changes in f(-x). Thus,
Thus, the sign changes from -34 to +5, +5 to -8, and ...
This shows how to find real and imaginary roots for polynomials up to degree 5.