Answer:
The polynomial function is [tex]x^{2} - 52[/tex]
Step-by-step explanation:
A polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = (x - x_{1})*(x - x_{2})[/tex].
In this problem:
The roots are [tex]x_{1} = 2\sqrt{13}[/tex] and [tex]x_{2} = -2\sqrt{13}[/tex]
Then
[tex](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[/tex]
The polynomial function is [tex]x^{2} - 52[/tex]
