Question

State how many imaginary and real zeros the function has.

Answer 1

Did anyone actually try just factoring it?

When I factor I get

f(x) = x^2(x+5) + 1(x+5)

Now I set f(x) = 0, to find some roots

0 = (x+5)(x^2 + 1)

Answer 2

ok
there is no positive root because no change of sign
now try this.
so \[f \left( -x \right)=-x ^{3+5x ^{2}}-x+5\]