CPM Homework Help : CCA2 Problem 8-87

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Home > CCA2 > Chapter 8 > Lesson 8.2.2 > Problem 8-87

8-87.

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

$-3 + i$ and $−3 − i$
Hint (a):
If these are the roots, what are the factors?
Step 1(a):
$y=\left(x-(-3+i)\right)\left(x-(-3-i)\right)$
Step 2(a):
$y=(x+3-i)(x+3+i)$
Multiply the factors.
You may want to use a generic rectangle.
The first row has been filled in for you.
Simplify after multiplying.
Possible Answer (a):
$f(x)=x^2+6x +10$

$5 +\sqrt { 3 }$ and $5 -\sqrt { 3 }$
Hint (b):
Use the same process as part (a).

$−2,$ $\sqrt { 7 }$ , and − $\sqrt { 7 }$
Hint (c):
What are the factors?
Step 1(c):
$y=(x-(-2))(x-\sqrt{7})(x+\sqrt{7})$
Step 2(c):
Multiply the last two factors first.
Then multiply the result by (x + 2).
Possible Answer (c):
$h(x)=x^3+2x^2-7x-14$

$4, -3 + i,$ and $−3 − i$
Hint (d):
Use the ideas from part (a) and (c) to help you.
How can you use the results from part (a) to make this problem easier?

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