Answer:
The given polynomial can have at most 8 roots.
Step-by-step explanation:
Here, the given polynomial is [tex]f (x) = x^{8} + 2x^{5} -3x + 4[/tex]
Now, by FUNDAMENTAL THEOREM OF ALGEBRA:
A polynomial of degree n can have at most n distinct real roots.
Here, the given polynomial is of degree 8. ( highest power of x)
So, by the stated theorem can have at most 8 roots which might or might not be distinct in nature.
