Let `f(x)= x^(3) + x + 1` and P(x) be a cubic polynomial such that P(0) = -1 and roots of f(0) = 1 ; P(x) = 0 are the squares of the roots of f(x) = 0 . Then find the value of P(4).

Explanation

To solve the problem, we need to find the value of \( P(4) \) given the polynomial \( f(x) = x^3 + x + 1 \) and the conditions about the polynomial \( P(x) \).

### Step 1: Identify the roots of \( f(x) \)
The polynomial \( f(x) = x^3 + x + 1 \) is a cubic polynomial. We need to find its roots, denoted as \( \alpha, \beta, \gamma \).

### Step 2: Calculate \( f(0) \)
To find the roots, we first evaluate \( f(0) \):
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