Question

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

Answer 1

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.