The given potential rational root is based on the factors of the constant
term and the leading coefficient.
- The function to which negative two-fifths is a potential root according to the rational root theorem is; <u>f(x) = 25·x⁴ - 7·x² + 4</u>
Reasons:
The given function are presented as follows;
f(x) = 4·x⁴ - 7·x² + x + 25
f(x) = 9·x⁴ - 7·x² + x + 10
f(x) = 10·x⁴ - 7·x² + x + 9
f(x) = 25·x⁴ - 7·x² + x + 4
The rational roots theorem is presented as follows;
The given potential rational root is
From the given options, the lead coefficient that has 5 as a factor are;
f(x) = 10·x⁴ - 7·x² + 9 and f(x) = 25·x⁴ - 7·x² + 4
From the two options above, the option that has a constant factor of 2 is the option; f(x) = 25·x⁴ - 7·x² + 4
Therefore;
- is a potential rational root of <u>f(x) = 25·x⁴ - 7·x² + 4</u>
Learn more about the rational root theorem here:
brainly.com/question/1578760