If a polynomial function f(x) has roots 3 and square root of 7, what must also be a root of f(x)?

Solution:

Given, a polynomial function f(x) has root 3 and √7.

Here, 3 is a real number.

√7 is an irrational number.

The root of the function always occurs in conjugate pairs.

Conjugate pair is a root which has two forms, one positive and one negative.

Example: a+√b and a-√b

For the given function f(x), √7 should be in conjugate pairs.

Other root of f(x) should be -√7

Therefore, the other root must be negative of root 7.

If a polynomial function f(x) has roots 3 and square root of 7, what must also be a root of f(x)?

Summary:

If a polynomial function f(x) has roots 3 and square root of 7, the other root must be -√7.