Find the difference between the roots of the quadratic equation x² + n²x - 122nx + 161x - 21 = 0 such that the sum of the roots of the equation is 4.

We use the identity (a - b)^2 = (a + b)^2 - 4ab to find the difference between the roots. The sum of the roots is given as a + b = 4, and from the equation x^2 - 120x - 21 = 0, the product of the roots is ab = -21. Substituting these into the identity gives (a - b)^2 = (4)^2 - 4(-21) = 16 + 84 = 100, so the positive difference between the roots is 10.

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