Answer:
One real root
Step-by-step explanation:
By the fundamental theorem of algebra, an nth degree polynomial has n-possible real roots.
If there are complex roots, then the the complex roots come in pairs.
Therefore the number of possible real roots of [tex]f(x)=x^3+2x^2+2x-5[/tex] are 3 real roots with no complex pairs or 1 real root with a complex pair.
By Descartes rule of signs, there is only one change of sign in the polynomial (+ to -).
Hence there is only one positive real root.
[tex]f(-x)=-x^3+2x^2-2x-5[/tex]
There is change is sign two times but we can not have even number of real roots for this polynomial
Therefore there is only real root.
