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 step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Identify the roots of the polynomial \( f(x) \)
Given the polynomial \( f(x) = x^3 + x + 1 \), we denote its roots as \( \alpha, \beta, \gamma \).

### Step 2: Write the polynomial \( P(x) \)
According to the problem, the roots of \( P(x) = 0 \) are the squares of the roots of \( f(x) = 0 \). Therefore, we can express \( P(x) \) as:
\[
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