Question

A polynomial function h(x) with integer coefficients has a leading coefficient of -5 and a constant term of -7. According to the Rational Root Theorem, which of the following are possible roots of h(x)?

a. 11/4
b. -7
c. -10
d. None of the above

Answer 1

The Rational Root Theorem helps determine possible roots of a polynomial function. The possible rational roots for h(x) are -7.

Step-by-step explanation:

The Rational Root Theorem can help us determine possible roots of a polynomial function with integer coefficients. According to the theorem, the possible rational roots of the function are the divisors of the constant term (-7) divided by the divisors of the leading coefficient (-5).

In this case, the divisors of -7 are 1 and 7, and the divisors of -5 are 1 and 5. So the possible rational roots are:

• a. 11/4: 11/4 is not a divisor of -7
• b. -7: -7 is a divisor of -7
• c. -10: -10 is not a divisor of -7
• d. None of the above

Therefore, the possible rational root of h(x) is -7.