Find all real value of a for which the equation `x^4 + (a - 1)x^3+ x^2 + (a - 1)x + 1 = 0` possesses at least two distinct positive roots

Explanation

To solve the equation \( x^4 + (a - 1)x^3 + x^2 + (a - 1)x + 1 = 0 \) for the values of \( a \) such that it possesses at least two distinct positive roots, we can follow these steps:

### Step 1: Analyze the given polynomial
The polynomial can be rewritten as:
\[ f(x) = x^4 + (a - 1)x^3 + x^2 + (a - 1)x + 1 \]
We want to find conditions on \( a \) such that \( f(x) = 0 \) has at least two distinct positive roots.
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