210k views
4 votes
15 POINTS!!!!! !!!!!! could i have some help on #39 with an explanation?? i just really don’t get it, lol. i thought i did, but then i looked at the answer key, and it is NOT what i thought. thank you guys so much, and happy halloween!!

15 POINTS!!!!! !!!!!! could i have some help on #39 with an explanation?? i just really-example-1
User OFFLlNE
by
8.4k points

1 Answer

5 votes

Hey there! In this problem, the solutions, both real and imaginary are provided. We have to work backwards to create a polynomial function which matches these solutions:

f(x) = (x - 6), (x + [5 + 2i]), (x + [5 - 2i])


Create a difference of squares,

f(x) = (x - 6), ([x + 5] + 2i), ([x + 5] - 2i)

f(x) = (x - 6), ([x + 5]^2 + 4)


[(x + 5)(x + 5)] + 4

x^2 + 5x + 5x + 25 + 4

x^2 + 10x + 29


f(x) = (x-6), (x^2 + 10x + 29)

f(x) = x^3 + 10x^2 + 29x - 6x^2 - 60x - 174

Combine like terms,

f(x) = x^3 + 4x^2 + 29x - 174


There we have our answer, a polynomial of degree 3.


f(x) = x^3 + 4x^2 + 29x - 174

User Ibrahim Hammed
by
8.0k points

Related questions

asked Feb 2, 2017 25.3k views
Matina asked Feb 2, 2017
by Matina
7.9k points
1 answer
2 votes
25.3k views
asked Jun 24, 2017 16.9k views
Tolbxela asked Jun 24, 2017
by Tolbxela
8.4k points
1 answer
1 vote
16.9k views
asked May 25, 2018 210k views
Dax Pandhi asked May 25, 2018
by Dax Pandhi
7.9k points
1 answer
3 votes
210k views
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.