Answer:
[tex]x=\pm i,x=-13[/tex]
Step-by-step explanation:
Since [tex]x=-1[/tex] is a solution of [tex]x^4+14x^3+14x^2+14x+13[/tex], by the factor theorem, [tex](x+1)[/tex] is a factor.
We perform the long division as shown in the attachment to obtain:
[tex]x^4+14x^3+14x^2+14x+13=(x+1)(x^3+13x+x+13)[/tex]
We now factor the cubic polynomial by grouping.
[tex]x^4+14x^3+14x^2+14x+13=(x+1)(x^2(x+13)+1(x+13))[/tex]
[tex]x^4+14x^3+14x^2+14x+13=(x+1)(x^2+1)(x+13)[/tex]
Hence the other roots are:
[tex]x=\pm i,x=-13[/tex]
