Question

Write a polynomial f(x) that meets the given conditions. Answers may vary.

Degree 2 polynomial with zeros of 3√10 and -3√10.

Answer 1

A degree 2 polynomial with zeros of 3√10 and -3√10 can be formed by multiplying the factors (x - 3√10) and (x + 3√10) which results in the polynomial f(x) = x² - 90.

Step-by-step explanation:

To write a degree 2 polynomial with zeros of 3√10 and -3√10, we can use the fact that if 'r' is a zero of a polynomial, then (x - r) is a factor of that polynomial. Given the zeros, we have two factors, (x - 3√10) and (x + 3√10). Multiplying these factors together gives us the polynomial:

f(x) = (x - 3√10)(x + 3√10)

Using the difference of squares pattern, we can expand this:

f(x) = x² - (3√10)²

f(x) = x² - 9×10

f(x) = x² - 90

Thus, the polynomial is x² - 90, which is a degree 2 polynomial with the given zeros.