Question

According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 – 2x4 + 9x3 – x2 + 12?

Answer 1

Answer:

Step-by-step explanation:

Given is an algebraic polynomial of degree 5.

$g(x) = 3x^5-2x^4+9x^3-x^2+12$

Here leading term is p=3 and constant term is q =12

Factors of p are ±1,±2,±3

Factors of q are $\frac{±1,±2,±3,±4,±6,±12}$

Possible forms of p/q will be the same for any other polynomial of degree 5 with leading term =3 and constant term = 12

Hence any other polynomial

$g(x) = 3x^5+ax^4+bx^3+cx^2+12$

will have same possible zeroes of p/q, when a,b,c are rational.

Hence any polynomial of this type would have the same possible rational roots.