p(x)=x^4-6x^3+14x^2-24x+40
two roots are r_1= 2i and r_2= 3-i. Doing no polynomial or synthetic division, do the following:
Find two more roots of p(x), and
Write a complete factorization of p(x)

Question

p(x)=x^4-6x^3+14x^2-24x+40
two roots are r_1= 2i and r_2= 3-i.  Doing no polynomial or synthetic division, do the following:
Find two more roots of p(x), and
Write a complete factorization of p(x)

blockcolder · Answer

Complex roots and irrational roots always come in pairs. If a+bi is a factor of P(x), then a-bi is also a factor.

anonymous · Answer

the other two roots are complex conjugate of  2i and 3-i
thus the other two roots are -2i  and 3+i
hence the complete factorisation 
can be written as (x-2i)(x+2i)(x-3+i)(x-3-i)
=(x^2+4)((x-3)^2+1)
=(x^2+4)(x^2 -6x +9+1)
=(x^2+4)(x^2 -6x +10)

anonymous · Answer

Thanks.

anonymous · Answer

welcome dear