Question

A polynomial function h(x) with integer coefficients has a leading coefficient of -2 and a constant term of -1. According to the Rational Root Theorem, which of the following are possible roots of h(x)?

Options:
A) 1
B) -1
C) 2
D) -2

Answer 1

According to the Rational Root Theorem, since the leading coefficient is -2 and the constant term is -1, the possible integer roots of the polynomial function can only be ±1. Therefore, the possible roots from the given options are 1 and -1.

Step-by-step explanation:

The question asks which of the given numbers could be possible roots of a polynomial function based on the Rational Root Theorem.

The Rational Root Theorem states that for a polynomial function with integer coefficients, if there is a rational number p/q (where p is an integer factor of the constant term and q is an integer factor of the leading coefficient) that is a root, then p must be a factor of the constant term, and q must be a factor of the leading coefficient.

In this case, the polynomial has a leading coefficient of -2 and a constant term of -1.

Therefore, the possible integer factors of the constant term (-1) are ±1, and the possible integer factors of the leading coefficient (-2) are ±2.

According to the Rational Root Theorem, the possible roots are the combinations of those factors, which are ±1 divided by ±2.

This simplifies to the roots being ±1 or ±0.5.

Since -0.5 is not one of the options provided and we are focusing on integer roots, the only possible integer roots from the given options that align with the Rational Root Theorem are 1 and -1.