time saver pack 2 - Algebra at its best

Blazing goIITian

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9 Apr 2009 21:20:24 IST
Posts: 1041
9 Apr 2009 21:20:24 IST
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time saver pack 2 - Algebra at its best

 Here's the second pack...

Algebra at its shortest best...

An equation axn + bxn-1 + cxn-2 + dxn-3 + ............................. + Qx + P = 0

will have n roots and sum of the roots--->

1. Taken 1 at a time =  

2. Taken 2 at a time = 

3. Taken 3 at a time = 

Taken n at a time = 

If n is odd sum will be negative, if n is even it will be positive.

**************************************************************************

A quadratic equation f(x) = ax2 + bx +c 

will be

1.   real

        Iff D = b2 - 4ac < 0

 

2. 

         = 

         When b2 - 4ac > 0

*************************************************************************

If b2 - 4ac > 0 and a > 0 then

-----------------f(x) > 0 for x <  or x < 

                       f(x) < 0 for  < x < 

                       f(x) = 0 for x =  or 

If b2 - 4ac > 0 and a < 0 then

-----------------f(x) < 0 for x <  or x > 

                       f(x) > 0 for  < x < 

                       f(x) = 0 for x =  or 

************************************************************************

If a > 0 then f(x) has least value at x = -b/2a

and value =

If a < 0 then f(x) has maximum value at x = -b/2a

and value = 

That's it.

Rate and comments awaited.

Watch out for pack 3

With nastiness

Mr. Nasty

 

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Blazing goIITian

Joined: 16 Jan 2009 18:51:57 IST
Posts: 1041
5 May 2009 11:50:44 IST
0 people liked this

..........................

Blazing goIITian

Joined: 12 Dec 2007 19:04:03 IST
Posts: 1249
5 May 2009 12:02:25 IST
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good.

Blazing goIITian

Joined: 14 Apr 2009 18:55:12 IST
Posts: 1263
30 Jun 2009 12:50:36 IST
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Gr8.

Blazing goIITian

Joined: 16 Jan 2009 18:51:57 IST
Posts: 1041
30 Jun 2009 12:57:38 IST
0 people liked this

Anytime....

Cool goIITian

Joined: 15 Jun 2009 04:50:32 IST
Posts: 84
30 Jun 2009 14:02:29 IST
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I can do better than this.

Blazing goIITian

Joined: 16 Jan 2009 18:51:57 IST
Posts: 1041
14 Mar 2010 18:26:56 IST
0 people liked this

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