A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

What is a 3rd degree polynomial function like f(0)=18 and whose zeros are -1, 2 ,and 3

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Your polynomial has the form: \[y=ax ^{3}+bx ^{2}+cx+d\] For f(0)=18 : your x=0 and y=18 \[y=a*0 ^{3}+b*0 ^{2}+c*0+d\] D=18 And the zeros are when your y=0 so , you have for x=-1 \[0=-a+b-c+d\] \[0=-a+b-c+18\] for x=2 \[0=8a+4b+2c+d\] \[0=8a+4b+2c+18\] for x=3 \[0=27a+9b+3c+d\] \[0=27a+9b+3c+18\] You need to solve this system of 3 equations to find a,b and c

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you can do it with matrices or by elimination

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks so much!!

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Try tipping those you help you out by pressing on that "Best Response" button to reward them a medal. Happy OpenStudying!

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \(\Large\rm\color{darkviolet}{\sideset{_\star~^\star}{~~_\star~^\star}{_\star}\hspace{-56pt}\color{blueviolet}{\overset{^\star~~~_\star~~~_\star~~~^\star~~~_\star~~~^\star~~~^\star}{^\star~^\star~~~ \star~~~~_\star~\star~_\star~~~^\star}\hspace{-35pt}}\color{bluepurple}{\underset{^\star~~~^\star~~~\star~~~_\star~~~\star~~~^\star~~~_\star~~~}{\star}}}\hspace{96pt}\Large\rm\color{darkviolet}{\sideset{_\star~^\star}{~~~~~~^\star}{_\star}\hspace{-129pt}\color{blueviolet}{\overset{^\star~~~_\star~~~_\star~~~^\star~~~_\star~~~^\star~~~^\star}{^\star~^\star~~~ \star~^\star~~\star~~~_\star~~~^\star}\hspace{-159pt}}\color{bluepurple}{\underset{^\star~~~^\star~~~\star~~~_\star~~~\star~~~^\star~~~_\star~~~}{\star}}}\hspace{-165pt}\LARGE\rlap{\it\color{red}{W}\color{orange}{e}\color{gold}{l}\color{lime}{c}\color{blue}{o}\color{blueviolet}{m}\color{purple}{e}\color{orchid}{~t}\color{magenta}{o}\color{red}{~O}\color{orange}{p}\color{gold}{e}\color{lime}{n}\color{cyan}{S}\color{blue}{t}\color{blueviolet}{u}\color{purple}{d}\color{orchid}{y}\color{magenta}{!}}{\hspace{-1.5pt}\it\color{black}{Welcome~to~OpenStudy!}}\) \(\it\color{charcoal}{~~~~Please~be~sure~to~read~OpenStudy's~terms~listed~within~the~following~links:}\) \(~\hspace{1.5pt}\large\color{red}{_✧~}\huge\color{orange}{^✧~}\normalsize\color{gold}{✧~~}\Large\color{blue}{/)}\LARGE\color{blue}{_∧}\Large\color{blue}{/)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}\hspace{-3.5pt}\Large\color{blueviolet}{/)}\LARGE\color{blueviolet}{_∧}\Large\color{blueviolet}{/)~~~~}\hspace{-10pt}\large\color{gold}{^✧}\LARGE\color{orange}{_✧}\huge\color{yellow}{^✧}\)\(~~\Large\color{red}{~~_✧~~}\large\rm\color{blue}{O(}\Large\color{blue}{^}\color{blue}{_ヮ}\hspace{-2pt}\Large\color{blue}{^}\hspace{-2pt}\color{blue}{)o}\hspace{160pt}\Large\rm\color{blueviolet}{o(}\Large\hspace{-3pt}\color{blueviolet}{^}\color{blueviolet}{_ヮ}\hspace{-2pt}\Large\color{blueviolet}{^~}\hspace{-3pt}\large\color{blueviolet}{)O}\small\color{orange}{~_✧}\Large\color{gold}{~~^✧}\hspace{-235.7pt}\underset{\href{https:///openstudy.com/terms-and-conditions}{\hspace{0pt}\LARGE\it{\color{red}{\bigstar~T}}\color{orange}{e}\color{gold}{r}\color{lime}{m}\color{cyan}{s}\color{blue}{~a}\color{blueviolet}{n}\color{purple}{d}\color{orchid}{~C}\color{magenta}{o}\color{pink}{n}\color{red}{d}\color{orange}{i}\color{gold}{t}\color{lime}{i}\color{cyan}{o}\color{blue}{n}\color{blueviolet}{s}\color{red}{~\bigstar}}}{{\href{https:///openstudy.com/code-of-conduct}{\hspace{5.5pt}\large\it{\color{red}{\bigstar~C}}\color{orange}{o}\color{gold}{d}\color{lime}{e~}\color{cyan}{o}\color{blue}{f~}\color{blueviolet}{C}\color{purple}{o}\color{orchid}{n}\color{magenta}{d}\color{pink}{u}\color{red}{c}\color{orange}{t}\color{red}{~\bigstar}}}}\) \(~\small\color{red}{~~~~~~~~_✧~~~~}\hspace{0pt}\large\rm\color{blue}{O(")(")~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}\hspace{0pt}\large\rm\color{blueviolet}{(")(")O}\small\color{red}{~~~~~~✧}\) \(\Large\color{green}{~~~~~⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒}\)

  6. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Try this:\[f(x) = k(x+1)(x-2)(x-3)\]\[f(0) = k\cdot1 \cdot (-2) \cdot (-3) = 6k = 18 \Rightarrow k = 3\]So\[f(x) = 3(x+1)(x-2)(x-3)\]

  7. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.