The conjugate which is 3 - √7 is also a root of f(x).
What is the root of a polynomial function?
The root of a polynomial function f(x) is the value of x for which f(x) = 0.
Now if a polynomial function has a root x = a + √b then the conjugate of x which is x' = a - √b is also a root of the function, f(x).
What must also be a root of f(x)?
Given that the polynomial function, f(x), with rational coefficients has roots
3 + √7, then by the above, the conjugate which is 3 - √7 is also a root of f(x).
So, 3 - √7 is also a root of f(x).
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