According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x³-7x+11? 0 +1.1.1.5 O 11 0 + 3.1.1.5, 45, +11 5 0 0 ±, ±3. 1. ±1, , 25, ±11

Answers 2

Answer:

1/5

-1/5

11/5

-11/5

1

-1

11

-11

Step-by-step explanation:

The Rational Root Theorem states that if a polynomial equation with integer coefficients has a rational root, then that root must be of the form p/q, where p is a factor of the constant term (in this case, 11) and q is a factor of the leading coefficient (in this case, 5).

Using this information, we can determine that the potential rational roots of the polynomial f(x) = 5x³-7x+11 are all of the following:

1/5

-1/5

11/5

-11/5

1

-1

11

-11

Note that this list includes all possible rational roots of the polynomial, but not all of these roots will necessarily be actual roots. To determine which of these potential rational roots are actual roots, we would need to test them by plugging them into the polynomial and solving for x.

AI generated Answer

The rational root theorem states that the potential rational roots of a polynomial equation of the form ax^n + bx^(n-1) + cx^(n-2) + ... + k = 0 are all the rational numbers that are in the form p/q where p is a factor of k (the constant term) and q is a factor of a (the leading coefficient). In this case, a = 5 and k = 11. This means that all the potential rational roots are all the rational numbers of the form p/q where p is a factor of 11 and q is a factor of 5. The factors of 11 are 1, -1, 11, and -11. The factors of 5 are 1, -1, 5, and -5. Therefore, the potential rational roots of the equation f(x) = 5x^3 - 7x + 11 are 0, ±1/5, ±3/5, ±1, ±3, 25, ±11.
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