Question

2. Find the roots of the polynomial equation.

2x3 + 2x2 – 19x + 20 = 0 (1 point) (more of the question in a moment)

Answer 1

\[\frac{ 3+i }{ 2 } , \frac{3-i}{2}, -4\]
\[\frac{ -3+2i }{ 2 } , \frac{-3-2i}{2}, 4\]
\[\frac{ -3+i }{ 2 } , \frac{-3-i}{2}, -4\]
\[\frac{ 3+2i }{ 2 } , \frac{3-2i}{2}, 4\]

Any help is appreciated! :)

Answer 2

There is a cubic root formula analogous to the quadratic equation used to solve polynomial roots for degree 2 equations. It can be found here:
http://www.math.vanderbilt.edu/~schectex/courses/cubic/
It is a pain in the retricethough. Is this a calculus based course?

Answer 3

here's a cheat way to do it...
according to the choices, one root is rational (either 4 or -4)... use synthetic division to figure out the quadratic when you divide your expression by (x+4) or (x-4).
then use the quadratic formula to find the complex roots.

Answer 4

@dpaInc yeah that works too, a nice quick was to do it when you know one root.