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

Answer:

The polynomial function is $x^{2} - 52$

Step-by-step 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 $x_{1} = 2\sqrt{13}$ and $x_{2} = -2\sqrt{13}$

Then

$(x - 2\sqrt{13}) \times (x - (-2\sqrt{13})) = (x - 2\sqrt{13}) \times (x + 2\sqrt{13}) = x^{2} - 2x\sqrt{13} + 2x\sqrt{13} -(2\sqrt{13})^{2} = x^{2} - 52$

The polynomial function is $x^{2} - 52$