186k views
2 votes
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the function in standard form. -2, 3, 6​

1 Answer

3 votes

Answer:

To write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 3, 6​, we can use the Linear Factorization Theorem1.

The theorem states that if a polynomial function f has zeros x = r1, x = r2, …, x = rn (where r1, r2, …, rn are distinct real numbers), then f(x) can be factored as follows:

f(x) = a(x - r1)(x - r2)…(x - rn)

where a is a nonzero constant.

So for this problem, we have:

f(x) = (x - (-2))(x - 3)(x - 6)

Multiplying this out gives:

f(x) = (x + 2)(x - 3)(x - 6)

Expanding this expression gives:

f(x) = x^3 - 7x^2 + 12x + 36

Therefore, the polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 3, 6​ is:

f(x) = x^3 - 7x^2 + 12x + 36

I hope this helps! Let me know if you have any other questions.

Explanation:

User Jwm
by
7.9k points

No related questions found