Find all the solutions of the equation p(x) = 0 if

p(x) = 3(x)^4 + 5(x)^3 + 25(x)^2 + 45x - 18

and 3i is one of the solutions.

Printable View

- Mar 23rd 2009, 05:45 PMNeedHelp18Another polynomial problem
Find all the solutions of the equation p(x) = 0 if

p(x) = 3(x)^4 + 5(x)^3 + 25(x)^2 + 45x - 18

and 3i is one of the solutions. - Mar 23rd 2009, 06:00 PMSoroban
Hello, NeedHelp18!

Quote:

Find all the solutions of: . if is one of the solutions.

If is a solution, then is also a solution.

. . Complex roots appear in conjugate pairs.

Then is a factor of the polynomial.

Using long division, we have: .

. . which factors further: .

Therefore, the roots are: .