Question

When using the rational root theorem, which of the following is a possible root of the polynomial function below? F(x)=2x^2-4x+9

Answer 1

Using the rational root theorem, we first look at the factors of a_n and a_0:

`\begin{gathered} a_0=9\text{ } \\ \text{Factors: 1,3,9}_{} \\ a_n=2 \\ \text{Factors: 1,2} \end{gathered}`

Now, finding the possible roots by matching the factors of a_0 with the factors of a_n we get:

`r=\frac{\text{factors of a\_0}}{\text{factors of a\_n}}=(1,3,9)/(1,2)=\mleft\lbrace1,3,9,(1)/(2),(3)/(2),(9)/(2)\mright\rbrace`

As we can see, a possible root of the polynomial solution is 3