Algebra

New kid on the Block

Joined: 10 Jun 2009
Post: 20
1 Mar 2012 10:17:23 IST
0 People liked this
5
1149 View Post
AIEEE Level- Quadratic Equations Questions-
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

1. If the equations and have a common root and a,b,c belong to N, find the minimum value of a+b+c.

 

2. If the equation does not have two distinct real roots and a + c>b, the prove that f(x) >= 0, for all x belonging to R.



Comments (5)


New kid on the Block

Joined: 10 Jun 2009
Posts: 20
1 Mar 2012 10:19:45 IST
0 people liked this

1. equations are

2. x2 + 3x +5=0 and ax2 +bx +c=0


New kid on the Block

Joined: 10 Jun 2009
Posts: 20
1 Mar 2012 10:20:12 IST
0 people liked this

I wonder why equations are not shown in my first post.
hemang's Avatar

Blazing goIITian

Joined: 27 Dec 2010
Posts: 1508
1 Mar 2012 15:25:24 IST
0 people liked this

x^2 + 3x+ 5 =0

clearly the roots are complex conjugates of each other.

so if ax^2 + bx + c = 0 and x^2 + 3x + 5 have a common root then their other roots are also equal.

so, a/1 = b/3 = c/5 = (a+b+c)/(1+3+5) = (a+b+c)/9.

a,b,c are natual numbers.

the minimum value is 5+3+1 = 9.

for the second question,

a + c - b > 0.

or, f(-1) > 0.

this might help.

i wanted to ask if a,b,c  are natural numers here like the first question?

sorry, but i am too dizzy to think anything...


New kid on the Block

Joined: 21 Mar 2012
Posts: 1
21 Mar 2012 13:24:44 IST
0 people liked this

AIEEE Level- Quadratic Equations Questions-
Bipin Dubey's Avatar

Forum Expert
Joined: 23 Jan 2007
Posts: 7958
5 Apr 2012 15:36:37 IST
0 people liked this

2. Since the equation doesn't have two distinct real roots : discriminant , D<=0

So the graph will either be above x-axis or touch it or it will be below x-axis or touch it

So, f(x) is either >=0 or <=0 for all x

f(-1) = a-b+c > 0, since for x=-1 it is positive therefore f(x)>=0




Quick Reply


Reply

Some HTML allowed.
Keep your comments above the belt or risk having them deleted.
Signup for a avatar to have your pictures show up by your comment
If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team
Free Sign Up!
Sponsored Ads

Preparing for JEE?

Kickstart your preparation with new improved study material - Books & Online Test Series for JEE 2014/ 2015


@ INR 5,443/-

For Quick Info

Name

Mobile

E-mail

City

Class

Vertical Limit

Top Contributors
All Time This Month Last Week
1. Bipin Dubey
Altitude - 16545 m
Post - 7958
2. Himanshu
Altitude - 10925 m
Post - 3836
3. Hari Shankar
Altitude - 10085 m
Post - 2217
4. edison
Altitude - 10825 m
Post - 7804
5. Sagar Saxena
Altitude - 8635 m
Post - 8064
6. Yagyadutt Mishr..
Altitude - 6330 m
Post - 1958

Find Posts by Topics

Physics

Topics

Mathematics

Chemistry

Biology

Parents Corner

Board

Fun Zone