Question

Find a polynomial function f(x) of degree 3 with real coefficients that satisfies the following conditions.
Zero of 0 and zero of 2 having multiplicity 2; f(3) = 15
The polynomial function is f(x) =
(Simplify your answer.)

Answer 1

Answer: The polynomial will be.

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 equation (1) we have

20 = A(5)(5 - 2)²

⇒

Therefore, the polynomial will be  (Answer)

Step-by-step explanation: