Question

List all rational roots for these polynomial equations:

x^3-x^2+2x-2=0
x^3=2x^2-8x-16=0

Find the roots of each polynomial equation:
2x^4-5x^3-17x^2+41x-21=0

A polynomial equation with rational coefficients has the given roots: find two additional roots.
sqrt(5) and -sqrt(13)
2 + 3i and 6i (As in imaginary numbers)

Find a third-degree polynomial equation with rational coefficients that has the given numbers as roots:
2 and -4i

Answer 1

Too many questions for one post :P

x^3-x^2+2x-2=0

Notice x=1 will work... 1-1 + 2 - 2 = 0. So you can divide off that zero with synthetic division.

You can also factor it by grouping:
\[\Large x^2(x-1) + 2(x-1) = 0\]