### Home > A2C > Chapter 9 > Lesson 9.2.2 > Problem9-89

9-89.

For each of the following sets of numbers, find the equation of a function that has these numbers as roots.

1. $−3 + i \text{ and } −3 − i$

If these are the roots, what are the factors?

$y = [x − \left(−3 + i\right)] [x − \left(−3 − i\right)]$

Mutiply the factors. You may want to use a generic rectangle. Simplify after multiplying.

$\textit{f}(\textit{x})=\textit{x}^2+6\textit{x}+10$

1. $5 + \sqrt { 3 }$ and $5 - \sqrt { 3 }$

Use the same process as part (a) above.

1. $−2,\sqrt { 7 }, \text{ and }- \sqrt { 7 }$

What are the factors?

$\textit{y} =\left( \textit{x}-(-2) \right) \left( \textit{x}-\sqrt{7} \right) \left( \textit{x}+\sqrt{7} \right)$

Multiply the last two factors first.

$\textit{h}(\textit{x})=\textit{x}^3+2\textit{x}^2-7\textit{x}-14$

1. $4, − 3 + i, \text{ and } −3 − i$

Use the ideas from part (a) and part (c) for this problem. How does part (a) make this problem reason