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

Question

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

Bytelearn · Accepted Answer

Understand Rational Root Theorem: The Rational Root Theorem states that any rational root, in the form of p/q (where p is a factor of the constant term and q is a factor of the leading coefficient), must be a factor of the constant term divided by a factor of the leading coefficient.List Factors of Constant Term: List all factors of the constant term -7: ±1, ±7.List Factors of Leading Coefficient: List all factors of the leading coefficient 2: ±1, ±2.Create Possible Fractions: Create all possible fractions p/q using the factors of -7 for p and the factors of 2 for q: ±1/1, ±7/1, ±1/2, ±7/2.Simplify Fractions: Simplify the fractions: -1, 1, -7, 7, -1/2, 1/2, -7/2, 7/2.Match to Given Choices: Match the simplified fractions to the given choices: (A) -1, (B) 1/2, (C) -1/2, (D) -7/2.

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