If the roots of `10 x^3-n x^2-54 x-27=0` are in harmonic progression, then `n` eqauls _________.

Explanation

To solve the problem, we need to find the value of \( n \) such that the roots of the polynomial \( 10x^3 - nx^2 - 54x - 27 = 0 \) are in harmonic progression (HP).

### Step-by-Step Solution:

1. **Understanding Harmonic Progression (HP)**:
- If the roots are in HP, then their reciprocals will be in arithmetic progression (AP). Let the roots be \( r_1, r_2, r_3 \). Then, \( \frac{1}{r_1}, \frac{1}{r_2}, \frac{1}{r_3} \) are in AP.

2. **Substituting for Roots**:
...