Solve `6x^(3)-11x^(2)+6x-1=0`, roots of the equatioin are in HP.

Explanation

To solve the equation \(6x^3 - 11x^2 + 6x - 1 = 0\) given that the roots are in Harmonic Progression (HP), we can follow these steps:

### Step 1: Understand the relationship of roots in HP
If the roots \(r_1, r_2, r_3\) are in HP, then their reciprocals \(y_1 = \frac{1}{r_1}, y_2 = \frac{1}{r_2}, y_3 = \frac{1}{r_3}\) are in Arithmetic Progression (AP).

### Step 2: Substitute \(x\) with \(\frac{1}{y}\)
To find the roots in terms of \(y\), we substitute \(x = \frac{1}{y}\) into the original equation:
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