A community for students.
Here's the question you clicked on:
 0 viewing
msingh
 2 years ago
SOLVE
if alpha and beta are zeroes of x^2+7x+K. find value of k
msingh
 2 years ago
SOLVE if alpha and beta are zeroes of x^2+7x+K. find value of k

This Question is Closed

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3anything else given for alpha and beta ? or you need k in terms of alpha and beta ?

myko
 2 years ago
Best ResponseYou've already chosen the best response.1Hint: \((x\alpha)(x\beta)=x^2+7x+K\)

msingh
 2 years ago
Best ResponseYou've already chosen the best response.0question has not sufficient data

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3well, product of roots(zeros) for ax^2+bx+c =0 is just c/a so here, k/1 = alpha*beta , gives k=alpha*beta

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.1\(\alpha + \beta = 7\) and \(\alpha \times \beta = k\)

myko
 2 years ago
Best ResponseYou've already chosen the best response.1\((x\alpha)(x\beta)=x^2(\alpha+\beta)x+\alpha\beta=x^2+7x+K\)\) can you finish this

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3still, you'll not get a value for k, you'll be able to express k in terms of either alpha or beta.

msingh
 2 years ago
Best ResponseYou've already chosen the best response.0@hartnn is absolutely correct

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.1I am trying to say something but checking my method first. It seems somewhat different .

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.1\((\alpha + \beta)^2 = 49\) \(\alpha^2 + \beta^2 + 2(k) = 49\) \(\alpha^2 + \beta^2 = 492k \) Now find : \((\alpha  \beta)^2 \) = \(\alpha^2 + \beta^2  2k\) = \(49  4k\) . So \(\alpha + \beta = 7\) and \(\alpha  \beta = \sqrt{494k}\)

myko
 2 years ago
Best ResponseYou've already chosen the best response.12 equations 3 unknowns.....

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.1\(2\alpha = 7 + \sqrt{494k}\) \(2\alpha + 7 = \sqrt{494k}\) \((2\alpha + 7)^2 = 494k\) \(4\alpha^2 + 49 + 28 \alpha = 49 4k\) \(4\alpha^2 + \cancel{49} + 28\alpha = \cancel{49}  4k\) \(4\alpha (\alpha + 7) = 4k\) \(k = \cfrac{\cancel{4}^{1}\alpha(\alpha+7)}{\cancel{4}^1} \) \(k = \alpha^2 7\alpha \)

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.1@myko yes but after simplifying we get much better answer for k in terms of only one root \(\alpha\) .

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3you could have got that by using : k= x^27x since, alpha (or beta) is a root, x= alpha k= alpha^27*alpha.

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.1I just presented my method . Though, there may be some arguments like its longer method or something else . But I just wanted to let the asker know about this method also. There may be many other methods to arrive the same answer that I given above, but if all the methods are known to a person, then it is better than knowing only 1 method , as per my opinion. Oh yeah, right Hartnn.

myko
 2 years ago
Best ResponseYou've already chosen the best response.1I don't see why it is better or worse... It is exactly same amount of info
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.