Answer:
2 complex roots
Step-by-step explanation:
The function f(x)=x^5+4x^3−5x can be factored as follows:
f(x)=x(x^4+4x^2−5). One root, a real root, is zero.
That leaves g(x) = x^4+4x^2−5. Substitute p = x^2, obtaining p^2 + 4p - 5 = 0. This factors as follows: (p+5)(p-1) = 0. Thus, p = -5 and p = 1.
Recalling that p = x^2, we have -5 = x^2 and +1 = x^2. The latter yields x = 1 and x = -1. The former yields +i√5 and =i√5.
Thus, the given poly has 3 real zeros: -1, 1 and 0. Due to the imaginary roots shown above, this means that this poly has 2 complex roots.
