Question

Select the correct answer from the drop-down menu.Find the polynomial,{4'" is the solution set of

Answer 1

Let P(x) be the polynomial such that the given set is its solution set.

Now notice that:

`\begin{gathered} x=-(1)/(3)\Rightarrow x+(1)/(3)=0\Rightarrow3x+1=0, \\ x=4\Rightarrow x-4=0. \end{gathered}`

Therefore (x-4) and (3x+1) divide to P(x), then:

`\begin{gathered} Exists\text{ k such that:} \\ P(x)=k(x-4)(3x+1). \end{gathered}`

Simplifying the above result we get:

`P(x)=k(3x^2-11x-4).`

Setting k=1 we get that:

`P(x)=3x^2-11x-4.`

Answer: Second option.