Respuesta :
Answer:
The polynomial will be [tex]f(x) = \frac{4}{9}x(x - 2)^{2}[/tex].
Step-by-step explanation:
The three degree polynomial function f(x) has zeros at x = 0 and at x = 4 having multiplicity 2.
Therefore, (x - 0) and (x - 4)² will be factors of the polynomial f(x).
Hence, the polynomial will be f(x) = Ax(x - 4)² .............. (1), where A is any constant that we have to evaluate.
Now, given that f(5) = 20
So, from the equation (1) we have
20 = A(5)(5 - 2)²
⇒ [tex]A = \frac{4}{9}[/tex]
Therefore, the polynomial will be [tex]f(x) = \frac{4}{9}x(x - 2)^{2}[/tex] (Answer)
Answer:
f(x)=4x(x-4)^2
Step-by-step explanation:
first we have a zero of 0, or (x-0) which can be simplified to just x
then we have a zero of 4 with a multiplicity of 2. thats (x-4) and since there's two we do (x-4)^2
so far we have f(x)=ax(x-4)^2
In order to find f(5)=30, we need to set X to 5. That changes it to a(5)(5-4)^2.
20=a(5)(5-4)^2.
a=4
so we plug the a value in and set X back. That gives us f(x)=4x(x-4)^2
