If a polynomial function f(x) has roots 0, 4, and 3 + StartRoot 11 EndRoot, what must also be a root of f(x)?

Step-by-step explanation:

If the polynomial function has rational coefficients, then the missing root must be conjugate with 3 + √11, which is achieved by reversing the sign of root:

Since 3 roots are rational but one of the four is irrational. Then, there must be a conjugate pair for that which we can do by reversing the sign between the rational and the non-rational part.

Hence, Another root of the polynomial function f(x) will be ofcourse the conjugate pair of 3 + √11 i.e. 3 - √11 (Ans)

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