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If a polynomial function, f(x), with rational coefficients has roots 3 and startroot 7 endroot, what must also be a root of f(x)?

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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).

Learn more about root of a polynomial function here:

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