BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Tough quadratic equation roots problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 141
Joined: Tue Oct 04, 2011 5:17 am
Thanked: 25 times

by coolhabhi » Wed May 23, 2012 11:27 am
Since (x - c) is a factor substitute x = c in the equation. (Because x - c = 0 which implies x = c)

so the equation transforms to
x^2 - 11x + 4c = 0
c^2 - 11c + 4c = 0
c^2 = 7c
c = 7

Now substitute c = 7 in the equation
x^2 - 11x + 4c = 0
x^2 - 11x + 28 = 0
The roots of which are 7 and 4.
So the larger root is 7
Answer is B

BTW what is the OA?
Top
Master | Next Rank: 500 Posts
Posts: 141
Joined: Tue Oct 04, 2011 5:17 am
Thanked: 25 times

by coolhabhi » Wed May 23, 2012 11:32 am
An other way to solve the problem might be this:

Since we know that (x - c) is a factor then one root will be c (Because x - c = 0 which implies x = c)

Let the other root be "y"

Now sum of the roots is 11 and product of the roots is 4c.
=>y + c = 11 and yc = 4c
From the above equations we get y = 4 and c = 7.

So the answer is B
Top
Post new topic Post Reply
• Page 1 of 1