In the case of polynomial functions with real coefficients, complex roots and irrational roots come in conjugate pairs. If a polynomial has a root that is an irrational number, like √7, then its conjugate must also be a root of the polynomial.
The conjugate of √7 is -√7. Therefore, if the polynomial function f(x) has roots 3 and √7, it must also have -√7 as a root. This ensures that the polynomial remains a function with real coefficients.