Question

According to the rational root theorem, negative seven-eighths is a potential rational root of which function? f(x) = 24x7 3x6 4x3 – x – 28 f(x) = 28x7 3x6 4x3 – x – 24 f(x) = 30x7 3x6 4x3 – x – 56 f(x) = 56x7 3x6 4x3 – x – 30

Answer 1

According to the rational root theorem, -7/8 is a potential rational root of: A. f(x) = 24x⁷ + 3x⁶ + 4x³ - x - 28.

What is a rational root theorem?

A rational root theorem is also referred to as rational root test and it states that when the coefficients of a polynomial are integers, all of the possible rational roots can be determined by dividing each factor of the constant term by each factor of the coefficient of the highest power (leading coefficient).

In Mathematics, the canonical form for a polynomial in one variable (x) is given by:

$a_n x^n + a_{n-1} x^{n-1} +a_1 x^1 +a_0=0$

Therefore, the potential rational root of the above polynomial is ±factors of a₀ dividided by ±factors of $a_n$ i.e ($\pm a_0/\pm a_n$).

For this exercise, -7/8 is a potential rational root of f(x) = 24x⁷ + 3x⁶ + 4x³ - x - 28 in accordance with rational root theorem;

• Factors of the leading coefficient are: 24: ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

• Factors of the constant term are: 28: ±1, ±2, ±4, ±7, ±14, ±28.

• Potential rational root is: ±7/8.

Read more on rational root theorem here: https://brainly.com/question/10937559

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