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

Solution

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

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

$f(x)=-\frac{1}{15}(x-3)^2(x+1)(x-5)$

Since the f(x) has degree 4

Hence the answer is :

$f(x)=-\frac{1}{15}(x-3)^2(x+1)(x-5)$