Let f(x) be a polynomial with integral coefficients. If f(1) and f(2) both are odd integers, prove that f(x) = 0 can' t have any integral root.

Explanation

To prove that the polynomial \( f(x) \) with integral coefficients cannot have any integral root given that \( f(1) \) and \( f(2) \) are both odd integers, we can follow these steps:

### Step 1: Assume \( k \) is an integral root of \( f(x) \)
Let’s assume that \( k \) is an integral root of the polynomial \( f(x) \). This means:
\[ f(k) = 0 \]

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