Question

Find the solutions to this equation algebraically using the Fundamental Theorem of Algebra, the Rational Root Theorem, Descartes' Rule of Signs, and the Factor Theorem. 4. 0=157x^3+628x^2-3768

Answer 1

the 4 isnt part of it

Answer 2

reference to the initial problem:
http://openstudy.com/study#/updates/4fa346d6e4b029e9dc3411df

Answer 3

divide all terms by 157 getting:\[x ^{3}+4x ^{2}-24=0\]For factor try 12 or 2 for the 24.
Divide by x-2 getting: \[x ^{2}+6x+12\] The factors are:
\[(x-2)(x ^{2}+6x+12)\] The solution of the real root is x=2, the two complex roots are the solution to the quadratic equation.

Answer 4

The complex roots are:\[x=-3\pm i \sqrt{3}\]

Answer 5

thankx you