1. The problem asks for the primary condition to apply the bisection method to find a root of a function $f(x)$. 2. The bisection method requires that the function $f(x)$ is continuous on the interval $[a,b]$ and that the function values at the endpoints satisfy $f(a) \cdot f(b) < 0$. 3. This condition ensures there is at least one root in the interval $[a,b]$ by the Intermediate Value Theorem, because the function changes sign between $a$ and $b$. 4. The other options are not necessary conditions: the root does not have to be at $x=0$, the function does not have to be a polynomial, and differentiability is not required (only continuity). 5. Therefore, the correct primary condition is option ii: $f(x)$ must be continuous on $[a,b]$ and $f(a) \cdot f(b) < 0$. Final answer: ii. $f(x)$ must be continuous on $[a,b]$ and $f(a) \cdot f(b) < 0$.