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satela [25.4K]
3 years ago
13

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

Mathematics
1 answer:
frosja888 [35]3 years ago
4 0

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)

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