### Home > CCA2 > Chapter 8 > Lesson 8.2.2 > Problem8-87

8-87.

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

1. $-3 + i$ and $−3 − i$

If these are the roots, what are the factors?

$y=\left(x-(-3+i)\right)\left(x-(-3-i)\right)$

$y=(x+3-i)(x+3+i)$

Multiply the factors.
You may want to use a generic rectangle.
The first row has been filled in for you.
Simplify after multiplying.

$f(x)=x^2+6x +10$

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

Use the same process as part (a).

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

What are the factors?

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

Multiply the last two factors first.
Then multiply the result by (x + 2).

$h(x)=x^3+2x^2-7x-14$

1. $4, -3 + i,$ and $−3 − i$