Question

Write a polynomial function that meets the given conditions. Answers may vary. Degree 2 polynomial with zeros of 2√ 13 and -2√13

Answer 1

The polynomial function is
`x^(2) - 52`

Explanation:

A polynomial has roots
`x_(1), x_(2)` such that
`ax^(2) + bx + c = (x - x_(1))*(x - x_(2))`.

In this problem:

The roots are
`x_(1) = 2√(13)` and
`x_(2) = -2√(13)`

Then

`(x - 2√(13)) * (x - (-2√(13))) = (x - 2√(13)) * (x + 2√(13)) = x^(2) - 2x√(13) + 2x√(13) -(2√(13))^(2) = x^(2) - 52`

The polynomial function is
`x^(2) - 52`