Poly (1 Viewer)

[fullonoob]

If z = -1/2 - root3 / 2 i is a root of z^4+2z^3 + z^2 - 1 = 0. find all the other roots.
WITHOUT using the quadratic form..cos dno how to use that.
hint : use conjugate

 

[scroates]

as coefficients are real one of the roots is -1/2 + root3 / 2 i

from here times z1 by z2 and by using the factor theorem z1xz2xz3xz4=e/a
and z1+z2+z3+z4=-b/a both z3 and z4 can be found

by the way left the working for you as doing the question yourself is much better for your learning than just seeing my solution.

 

[fullonoob]

as coefficients are real one of the roots is -1/2 + root3 / 2 i

from here times z1 by z2 and by using the factor theorem z1xz2xz3xz4=e/a
and z1+z2+z3+z4=-b/a both z3 and z4 can be found

by the way left the working for you as doing the question yourself is much better for your learning than just seeing my solution.

ehh dno the e/a thing
though i know you can do it by finding -b/a c/a -d/a but too long
thx anyways learnt how to do the quadratic, just didn't see it properly

 

[scroates]

or you can find the other roots by finding the quadratics with roots z1 and z2, then use polynomial division to find a quadratic expression with roots z3 and z4

 

[Trebla]