Polynomials

[joodr]

Given p(x)= 3x^4-36x^3+186x^2-486x+507
1.1 determine all of the polynomial's roots, knowing that it has a double multiplicity complex root.
1.2 factorize completely in C, R and Q


I need help with this exercise. I don't know how to determine its complex roots.

 

[Dr.Peterson]

What would it mean if it has a complex root with multiplicity 2, in terms of its factorization? Try writing that out with unknown coefficients, and equate that to the given polynomial.

 

[Steven G]

Hi, where did this problem come from? Whoever made up the problem was not very careful. This polynomial has two real roots and two complex roots. As always the complex roots are conjugates of one another.

 

[Dr.Peterson]

Hi, where did this problem come from? Whoever made up the problem was not very careful. This polynomial has two real roots and two complex roots. As always the complex roots are conjugates of one another.

I hadn't checked it, but you're right.

That explains why my attempt to carry out my suggested plan didn't work.