Respuesta :
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; f(x) = 25·x⁴ - 7·x² + 4
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;
- [tex]\displaystyle Possible \ rational \ roots = \mathbf{\frac{The \ constant \ factors }{The \ lead \ coefficient \ factors}}[/tex]
The given potential rational root is [tex]\displaystyle \mathbf{-\frac{2}{5}}[/tex]
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;
- [tex]\displaystyle -\frac{2}{5}[/tex] is a potential rational root of f(x) = 25·x⁴ - 7·x² + 4
Learn more about the rational root theorem here:
https://brainly.com/question/1578760
