Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
ronocthede
Group Title
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?
 9 months ago
 9 months ago
ronocthede Group Title
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?
 9 months ago
 9 months ago

This Question is Closed

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

ronocthede Group TitleBest ResponseYou've already chosen the best response.0
Okay so I assume I use substitution here?
 9 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
you 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 ?
 9 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
find PQ now
 9 months ago

ronocthede Group TitleBest ResponseYou've already chosen the best response.0
Hmm I think so. So PQ = 5/8 ?
 9 months ago

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

hartnn Group TitleBest ResponseYou've already chosen the best response.2
then simplify
 9 months ago

ronocthede Group TitleBest ResponseYou've already chosen the best response.0
okay 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?
 9 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
thats 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
 9 months ago

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

hartnn Group TitleBest ResponseYou've already chosen the best response.2
to find PQ ? not much, you can try
 9 months ago

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

whpalmer4 Group TitleBest 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
 9 months ago

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

whpalmer4 Group TitleBest ResponseYou've already chosen the best response.1
and 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.
 9 months ago

whpalmer4 Group TitleBest ResponseYou've already chosen the best response.1
I still like @hartnn's approach best, though
 9 months ago

ronocthede Group TitleBest ResponseYou've already chosen the best response.0
Thanks again, really helped clear it up.
 9 months ago
See more questions >>>
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.