Respuesta :
Answer:
Neither expression satisfies the given rational root.
Step-by-step explanation:
To find the right answer, we just need to replace the given root in each expression and see which one gives zero.
First expression.
[tex]f(x)=4x^{4} -7x^{2} +x+25\\f(-\frac{2}{5})= 4(-\frac{2}{5})^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+25=\frac{64}{625}-\frac{28}{25} -\frac{2}{5} +25 \approx 23.58[/tex]
Second expression.
[tex]f(x)=9x^{4}-7x^{2} +x+10=9(-\frac{2}{5} )^{4} -7(-\frac{2}{5} )^{2} +\frac{2}{5} +10 \approx 9.5[/tex]
Third expression.
[tex]f(x)=10x^{4}-7x^{2} +x+9=10(-\frac{2}{5} )^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+9 \approx 7.7[/tex]
Fourth expression.
[tex]f(x)=25x^{4}-7x^{2} +x+4=25(-\frac{2}{5} )^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+4 \approx 3.12[/tex]
Therefore, neither expression satisfies the given rational root.
Answer:
D. f(x) = 25x^4 - 7x^2 + x + 4.
Step-by-step explanation:
The correct answer to your question is D.
