Question

Find a polynomial function f(x) of degree 3 with real coefficients that satisfies the following conditions.

Answer 1

Answer:

The polynomial will be $f(x) = \frac{4}{9}x(x - 2)^{2}$.

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

⇒ $A = \frac{4}{9}$

Therefore, the polynomial will be $f(x) = \frac{4}{9}x(x - 2)^{2}$ (Answer)