A polynomial function g(x) with integer coefficients has a leading coefficient of -14 and a constant term of 1. According to the Rational Root Theorem, which of the following are possible roots of g(x)? Multi-select Choices: (A)15/2 (B)15/7 (C)-1/2 (D)1/14

Question

A polynomial function g(x) with integer coefficients has a leading coefficient of -14 and a constant term of 1. According to the Rational Root Theorem, which of the following are possible roots of g(x)?   Multi-select Choices: (A)15/2 (B)15/7 (C)-1/2 (D)1/14

Bytelearn · Accepted Answer

Rational Root Theorem: The Rational Root Theorem states that any rational root, in the form of p/q, must have p as a factor of the constant term and q as a factor of the leading coefficient.Constant Term Factors: List the factors of the constant term 1: ±1.Leading Coefficient Factors: List the factors of the leading coefficient -14: ±1, ±2, ±7, ±14.Generate Possible Roots: Generate all possible rational roots by combining the factors of the constant term with the factors of the leading coefficient: ±1/1, ±1/2, ±1/7, ±1/14.Simplify Roots List: Simplify the list of possible rational roots: ±1, ±1/2, ±1/7, ±1/14.Compare with Given Choices: Compare the simplified list of possible rational roots with the given choices to determine which ones are correct: (A) 15/2 is not a possible root because 15 is not a factor of 1. (B) 15/7 is not a possible root because 15 is not a factor of 1. (C) -1/2 is a possible root because -1 is a factor of 1 and 2 is a factor of -14. (D) 1/14 is a possible root because 1 is a factor of 1 and 14 is a factor of -14.

Full solution

More problems from Rational root theorem

Related topics