39.2k views
3 votes
Write the polynomial function of least degree that has zeros of x=-3, x= square root of 6, and x= -square root of 6

User Lukeck
by
7.8k points

1 Answer

4 votes

Final answer:

The polynomial function of least degree with zeros x = -3, x = √6, and x = -√6 is given by P(x) = (x + 3)(x² - 6) or P(x) = x³ + 3x² - 6x - 18.

Step-by-step explanation:

The question is asking for a polynomial function of least degree with given zeros. To find this polynomial, we can use the zeros x = -3, x = √6, and x = -√6. We know that for a zero at x = a, the factor of the polynomial will be (x - a). Therefore, we can write the polynomial as:

P(x) = (x + 3)(x - √6)(x + √6).

Since (x - √6)(x + √6) is a difference of squares, it simplifies to x² - 6. The polynomial function of least degree that includes all given zeros is then:

P(x) = (x + 3)(x² - 6) = x³ + 3x² - 6x - 18.

This is the required polynomial function.

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