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

Solution:

A polynomial function f(x) has √3 and √7

√3 and √7 is an irrational number

The zeroes or root of a function occurs in conjugate pairs.

A conjugate pair is where a root contains two forms, one positive and negative

a + √b and a - √b

√3 and √7 should be in conjugate pair in the given function

Another possible root is - √3 and - √7

Therefore, the root of f (x) is - √3 and - √7.

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

Summary:

If a polynomial function f(x) has √3 and √7, - √3 and - √7 is also a root of f (x).