A polynomial function, f(x), with rational coefficients has roots of –2 and square root of 3. The irrational conjugates theorem

Question

tangare [24]

3 years ago

11

A polynomial function, f(x), with rational coefficients has roots of –2 and square root of 3. The irrational conjugates theorem

states that which of the following must also be a root of the function?

Mathematics

2 answers:

kap26 [50] · Answer 1 · 2022-09-02T20:08:29+03:00

kap26 [50]3 years ago

8 0

Answer:

Step-by-step explanation:

option b

makkiz [27] · Answer 2 · 2022-09-02T21:57:58+03:00

Answer:if 2 + √3 is an irrational root to a polynomial, then its irrational conjugate 2- √3 is also.

Step-by-step explanation:

Given : A polynomial function, f(x), with rational coefficients has roots of –2 and square root of 3.

To find : which of the following must also be a root of the function?

Solution : We have root of f(x) = 2 +√3.

By the irrational conjugates theorem : it state that states that if a + √b is an irrational root to a polynomial, then its irrational conjugate a - √b is also

root.

Therefore, if 2 + √3 is an irrational root to a polynomial, then its irrational conjugate 2- √3 is also.