Question

A polynomial function g(x) with integer coefficients has a leading coefficient of -6and a constant term of 9. According to the Rational Root Theorem, which of thefollowing are possible roots of g(x)?

Answer 1

Given:

it is given that a polynomial function g(x) with integer coefficients has a leading coefficient of -6 and a constant term of 9.

Find:

we have to find the correct root of the function from the given options.

Step-by-step explanation:

Following is the statement of Rational root theorem

Therefore, according to the Rational root theorem

(-2/3) , (-2/9), 2 are the possible roots of g(x)

as gcd(-2,3) = 1 and -2|-6 & 3|9

gcd(-2,9) = 1 and -2|-6 & 9|9

gcd(2,1) = 1 and 2|-6 & 1|9.

Therefore, the possible roots of the polynomial g(x) are (-2/3) , (-2/9), 2.