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Algebra

Blazing goIITian

Joined:	10 Jun 2007
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1 Apr 2009 20:52:41 IST

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303

Theory of equations

None

Let a, b, c be the roots of f(x) = x³ + x² - 5x - 1 = 0. Then [a] + [b] + [c], where [.] denotes GIF, is equal to

(a) 1

(b) -2

(d) -3

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Comments (5)

Sameer Chetiwal

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Joined: 26 Jan 2009

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1 Apr 2009 21:11:07 IST

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Its -3 dude.

Result

Sahil Gupta

Blazing goIITian

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Posts: 985

1 Apr 2009 21:42:28 IST

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Is this valid for only this particular equation or for any equation? and how to prove it?

Sameer Chetiwal

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Joined: 26 Jan 2009

Posts: 27

1 Apr 2009 21:49:37 IST

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u can solve such type of questions by just drawing the graphs of the equations.

akshay A NEW BEGINNING...

Blazing goIITian

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1 Apr 2009 23:48:23 IST

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x^3 - x^2 - 5x - 1

finding derivative
3x^2 - 2x - 5 = 0
hence -1 is maxima and 5/3 is minima.

the value at 1- is 2
and value at 0 is -1
hence graph will cut x axis between 0 and -1.
hence greatest integer = -1

similarly at -1 value is positive
and at -2 it is negative
hence graph will cut x axis between -1 and -2
hence greatest integer is -2

also value at 2 is negative and 3 is positive
hence graph will cut x axis between 2 and 3
hence greatest integer is 2
.
hence [sum of all root ] = -1 -2+2 = -1..=--- ans...

akshay A NEW BEGINNING...

Blazing goIITian

Joined: 25 Dec 2007

Posts: 1104

1 Apr 2009 23:50:02 IST

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ohh soorryy i misread the Q...i that is + x^2 i have solved it taking -x^2...however method remains same.

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