Question

the graph of the polynomial f(x) is given below. If f(x) has degree 4, find the factored equation for f(x).Check Picture

Answer 1

The graph of the polynomial f(x) is given below. If f(x) has degree 4, find the factored equation for f(x).

Given graph solution as degree is 4

The four roots are x = -1 , x = 3, x = 3, x = 5 where the graph passes through x-axis

`\begin{gathered} f(x)=A(x-3)^2(x+1)(x-5) \\ when\text{ x = 0, y =3} \\ 3=A(-3)^2(1)(-5) \\ 3=-45A \\ A=-(1)/(15) \end{gathered}`

`f(x)=-(1)/(15)(x-3)^2(x+1)(x-5)`

Since the f(x) has degree 4

Hence the answer is :

`f(x)=-(1)/(15)(x-3)^2(x+1)(x-5)`