Question

According to the Rational Root Theorem, Negative two-fifths is a potential rational root of which function? f(x) = 4x4 â€" 7x2 x 25 f(x) = 9x4 â€" 7x2 x 10 f(x) = 10x4 â€" 7x2 x 9 f(x) = 25x4 â€" 7x2 x 4.

Answer 1

Answer:

D. f(x) = 25x^4 - 7x^2 + x + 4.

Step-by-step explanation:

Answer 2

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;

• $\displaystyle Possible \ rational \ roots = \mathbf{\frac{The \ constant \ factors }{The \ lead \ coefficient \ factors}}$

The given potential rational root is $\displaystyle \mathbf{-\frac{2}{5}}$

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;

• $\displaystyle -\frac{2}{5}$ is a potential rational root of f(x) = 25·x⁴ - 7·x² + 4

Learn more about the rational root theorem here:

brainly.com/question/1578760