In a triangle ABC, if the sides a,b,c, are roots of `x^3-11 x^2+38 x-40=0,` then find the value of `(cosA)/a+(cosB)/b+(cosC)/c`

Explanation

To solve the problem, we need to find the value of \(\frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c}\) given that the sides \(a\), \(b\), and \(c\) are the roots of the polynomial \(x^3 - 11x^2 + 38x - 40 = 0\).

### Step 1: Find the roots of the polynomial
The roots of the polynomial \(x^3 - 11x^2 + 38x - 40 = 0\) can be found using Vieta's formulas:
- The sum of the roots \(a + b + c = 11\)
- The sum of the product of the roots taken two at a time \(ab + bc + ca = 38\)
- The product of the roots \(abc = 40\)

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