176k views
4 votes
Find a polynomial function of degree 3 with real coefficients and zeros of -3, -1, and 4, for which f(-2)=-24

User Tyre
by
7.8k points

1 Answer

4 votes

Answer:

The answer is:

f(x) = -4x^3 + 52x + 48

Explanation:

Since the polynomial has zeros at -3, -1, and 4, it can be written in the form:

f(x) = a(x + 3)(x + 1)(x - 4)

where a is a real coefficient.

We are given that f(−2)=−24. Substituting x=−2 into the above equation, we get:

-24 = a(-2 + 3)(-2 + 1)(-2 - 4)

Simplifying both sides, we get a=−4.

Therefore, the polynomial function we are looking for is:

f(x) = -4(x + 3)(x + 1)(x - 4)

This can also be written in standard form as:

f(x) = -4x^3 + 52x + 48

User Kaarto
by
8.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories