Question

Prove that the function f(x) = x¹⁰¹ * x⁵¹ * 1 has neither:

a) Real roots
b) Imaginary roots
c) Both real and imaginary roots
d) All of thw above

Answer 1

The function f(x) = x¹⁰¹ * x⁵¹ * 1 has neither real roots nor imaginary roots.

Step-by-step explanation:

The function f(x) = x¹⁰¹ * x⁵¹ * 1 has only one term, which is 1. In order for a function to have real roots, the function must equal zero at some point. Since the function is always equal to 1, it will never be equal to zero and therefore does not have any real roots.

Similarly, in order for a function to have imaginary roots, the function must have a negative value at some point. Since the function is always equal to 1, it will never be negative and therefore does not have any imaginary roots.

Based on these observations, the function f(x) = x¹⁰¹ * x⁵¹ * 1 has neither real roots nor imaginary roots.