It is currently 25 Jun 2017, 00:22

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A,B are roots of equation (x)(x)-px+q=0. A,C are roots of

Author Message
Manager
Joined: 28 Jun 2004
Posts: 90
A,B are roots of equation (x)(x)-px+q=0. A,C are roots of [#permalink]

### Show Tags

30 Oct 2004, 13:11
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A,B are roots of equation (x)(x)-px+q=0. A,C are roots of equation (x)(x)-qx+p=0. Find the equation whose roots are B and C.
Director
Joined: 16 Jun 2004
Posts: 891

### Show Tags

30 Oct 2004, 21:33
This may not be a GMAT type question. However, here's how to solve.
Note: quadratic equation can be represented as a1x+b1x+c1 = 0

The common root between the two quadratic is given as A.

Common root (here A) is given by (c1a2-c2a1)/(a1b2-a2b1) = (q-p)/(-q+p) = -1.

From equations we have
AB = q and AC = p (Note: sum of roots = -b/a. Product of roots = c/a)
=>B=-q (since A=-1) and C = -p.
We have the roots B and C.

Also, in any quadratic the euation is essentially

x^2 -(sum of roots)x + product of roots = 0

sum of roots = -b/a. Product of roots = c/a

So, the new quadratic equation is
x^2 -(p+q)x +pq = 0.
Senior Manager
Joined: 06 Dec 2003
Posts: 366
Location: India

### Show Tags

31 Oct 2004, 03:38
x^2 + (p+q)x + pq

I did this one by solving two equations on A.
A = -1 is correct
so
B = -q and C = -p => B + C = -p-q = -(p+q) & BC = pq

So equations with B anc C as a roots is:

x^2 - (B+C)x + BC = x^2 + (p+q)x + pq

cheers,
Dharmin
_________________

Perseverance, Hard Work and self confidence

Director
Joined: 16 Jun 2004
Posts: 891

### Show Tags

31 Oct 2004, 04:41
Dharmin wrote:
answer should be: x^2 + (p+q)x + pq

Agree. Silly mistake from my end.
31 Oct 2004, 04:41
Display posts from previous: Sort by

# A,B are roots of equation (x)(x)-px+q=0. A,C are roots of

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.