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1. 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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