A community for students.
Here's the question you clicked on:
 0 viewing
ronocthede
 one year ago
Now sure how to get to answer:
A quadratic function, f, has zeros P and Q such that P+Q=5 and (1/P)+(1/Q)=8. What function would best describes f?
ronocthede
 one year ago
Now sure how to get to answer: A quadratic function, f, has zeros P and Q such that P+Q=5 and (1/P)+(1/Q)=8. What function would best describes f?

This Question is Closed

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2so you have sum of roots find product of roots PQ from (1/P)+(1/Q)=8. can u ?

ronocthede
 one year ago
Best ResponseYou've already chosen the best response.0Okay so I assume I use substitution here?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2you can, yes. but see this : 1/P + 1/Q =8 (Q+P)/PQ = 8 we know P+Q = 5 so, 5/(PQ) = 8 got this ?

ronocthede
 one year ago
Best ResponseYou've already chosen the best response.0Hmm I think so. So PQ = 5/8 ?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2now , equation will be \(x^2 (P+Q)x + PQ = 0\)

ronocthede
 one year ago
Best ResponseYou've already chosen the best response.0okay so 8x^240x+5, which I know is the right answer. I'm still a bit confused where "x^2−(P+Q)x+PQ=0" Is that a formula I forgot?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2thats a standard relation. like if you have x^2 +ax+b = 0 sum of roots will be a and product of roots = b thats where it came from

ronocthede
 one year ago
Best ResponseYou've already chosen the best response.0Oh yeah, I vaguely remember that. One more thing sorry, how difficult would the substitution be?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2to find PQ ? not much, you can try

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2a longer way will be to actually find the values of P and Q. then equation will be (xP)(xQ) = 0 then simplify

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.1\[f(x)=(xP)(xQ)\]is just the polynomial in factored form \[f(x)=(xP)(xQ) = x^2QxPx+PQ = x^2(P+Q)x + PQ\] after expansion and collecting like terms

ronocthede
 one year ago
Best ResponseYou've already chosen the best response.0Okay that makes a lot of sense. Was just blanking out there. Thanks for the help guys!

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.1and substitution isn't too bad: \[P+Q=5\]\[P=5Q\]\[\frac{1}P+\frac{1}Q =8\]\[\frac{1}{5Q}+\frac{1}Q =8\]Multiply everything by \(Q(5Q)\) to get \[Q+5Q = 8Q(5Q)\]\[8Q^2+40Q5=0\]Etc.

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.1I still like @hartnn's approach best, though

ronocthede
 one year ago
Best ResponseYou've already chosen the best response.0Thanks again, really helped clear it up.
Ask your own question
Sign UpFind more explanations on OpenStudy
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
 Engagement 19 Mad Hatter
 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.