According to the Rational Root Theorem, -2/5 is a potential rational root of which function?
f(x) = 4x⁴ - 7x² + x + 25
f(x) = 9x⁴ - 7x² + x + 10
f(x) = 10x⁴ - 7x² + x + 9
f(x) = 25x⁴ - 7x² + x + 4

Solution:

We have to find -2/5 is a potential rational root of which of the given functions.

From the options,

a) f(x) = 4x⁴ - 7x² + x + 25

The factors of constant term 25 are 1, 5, 25

The factors of leading coefficient 4 are 1, 2, 4

Ratios are (± 1, 5, 25)/(± 1, 2, 4)

Therefore, -2/5 is not a potential root of the function f(x).

b) f(x) = 9x⁴ - 7x² + x + 10

The factors of constant term 10 are 1, 2, 5, 10

The factors of leading coefficient 9 are 1, 3, 9

Ratios are (± 1, 2, 5, 10)/(± 1, 3, 9)

Therefore, -2/5 is not a potential root of the function f(x).

c) f(x) = 10x⁴ - 7x² + x + 9

The factors of constant term 9 are 1, 3, 9

The factors of leading coefficient 10 are 1, 2, 5, 10

Ratios are (± 1, 3, 9)/(± 1, 2, 5, 10)

Therefore, -2/5 is not a potential root of the function f(x).

d) f(x) = 25x⁴ - 7x² + x + 4

The factors of constant term 4 are 1, 2, 4

The factors of leading coefficient 25 are 1, 5, 25

Ratios are (± 1, 2, 4)/(± 1, 5, 25)

Therefore, -2/5 is a potential root of the function f(x).

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According to the Rational Root Theorem, -2/5 is a potential rational root of which function?

Summary:

According to the Rational Root Theorem, -2/5 is a potential rational root of f(x) = 25x⁴ - 7x² + x + 4