if ` alpha, beta, gamma ` are the roots of the equation ` x^(3) + 3x + 2=0 " then " (alpha^(3) +beta^(3)+gamma^(3))/(alpha^(2) +beta^(2)+gamma^(2))`

Explanation

To solve the problem, we need to find the value of the expression \(\frac{\alpha^3 + \beta^3 + \gamma^3}{\alpha^2 + \beta^2 + \gamma^2}\) given that \(\alpha, \beta, \gamma\) are the roots of the polynomial \(x^3 + 3x + 2 = 0\).

### Step 1: Identify the coefficients
From the polynomial \(x^3 + 0x^2 + 3x + 2 = 0\), we can identify the coefficients:
- \(a = 1\) (coefficient of \(x^3\))
- \(b = 0\) (coefficient of \(x^2\))
- \(c = 3\) (coefficient of \(x\))
- \(d = 2\) (constant term)
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