Answer :

The roots of the polynomial function f(x) = 7x^4 - 48x^3 + 42x^2 - 1 are 1, -1/7, 3 - 2√2, and 3 + 2√2.

To find the roots of a polynomial like this, we can use various methods such as factoring, the rational root theorem, and synthetic division.

In this case, it appears that the roots were found using either a numerical root-finding method or perhaps factoring.

The polynomial appears to be factored into its irreducible factors, which are (x - 1), (7x + 1), (x - (3 - 2√2)), and (x - (3 + 2√2)).

Therefore, the roots are 1 (from x - 1), -1/7 (from 7x + 1), and the two remaining roots are from solving the equations x - (3 - 2√2) = 0 and x - (3 + 2√2) = 0.

These roots are 3 - 2√2 and 3 + 2√2. This is how the roots were determined.

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