If the roots of the equation `10x^(3)-cx^(2)-54x-27=0` are in harmonic progression the value of c is

Explanation

To find the value of \( c \) such that the roots of the equation \( 10x^3 - cx^2 - 54x - 27 = 0 \) are in harmonic progression, we can follow these steps:

### Step 1: Understand the relationship between roots in HP and AP
If the roots \( a, b, c \) are in harmonic progression, then their reciprocals \( \frac{1}{a}, \frac{1}{b}, \frac{1}{c} \) are in arithmetic progression (AP).

### Step 2: Use Vieta's formulas
From Vieta's formulas for the cubic equation \( 10x^3 - cx^2 - 54x - 27 = 0 \), we know:
- The sum of the roots \( a + b + c = \frac{c}{10} \)
...