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Saurabh123
Joined: 28 Jun 2006
Posts: 4
Location: Fbd
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 Posted: Tue Jul 04, 2006 12:28 pm Post subject: Sum of roots, product of roots etc. of some polynomial |
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Hi guys,
we know that for a quadratic eqn, ax^2+bx+c=0,
sum of roots = -b/a, product of roots = c/a
What bt for a cubic eqn?? ax^3+bx^2+cx+d=0
and in particular how to find
-sum,
-product taken 2 roots at a time
-product taken 3 roots at a time.....and other such things
for a general eqn. ax^n+bx^n-1+cx^n-2+.....+g=0
thnx,
Saurabh |
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Saurabh123
Joined: 28 Jun 2006
Posts: 4
Location: Fbd
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| Posted: Wed Jul 05, 2006 10:25 am Post subject: Re: Sum of roots, product of roots etc. of some polynomial |
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Hi,
koi to reply karo!!! |
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CZ@@@H@@@R
Serious about CAT
Joined: 14 Jan 2006
Posts: 64
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| Posted: Thu Jul 06, 2006 2:44 pm Post subject: Sum of roots, product of roots etc. of some polynomial |
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| Quote: |
Hi guys,
we know that for a quadratic eqn, ax^2+bx+c=0,
sum of roots = -b/a, product of roots = c/a
What bt for a cubic eqn?? ax^3+bx^2+cx+d=0
and in particular how to find
-sum,
-product taken 2 roots at a time
-product taken 3 roots at a time.....and other such things
for a general eqn. ax^n+bx^n-1+cx^n-2+.....+g=0
thnx,
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an x^n+ an-1 x^n-1 + an-2 x^n-2 + .. a1 x ...+ a0 = 0
n, n-1, .... are subscripts to a
Sum(one root at a time) = - an-1 / an
Sum(Two roots at a time) = an-2 / an
.
.
.
Sum(k roots at a time) = (-1)^k an-k / an |
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g2
Joined: 01 Aug 2006
Posts: 4
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| Posted: Thu Aug 03, 2006 10:04 pm Post subject: |
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hi
i just know that the no. of solution we have for an equation like that is simply the power of its 1st variable like----------
a x^3+bx^2+cx+d=0 then the no. of solution will be 3 and so on.....
i think u have asked that only |
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kunalkapse
Joined: 08 Jul 2006
Posts: 4
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| Posted: Mon Aug 07, 2006 2:40 am Post subject: reply |
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hi saurabh
i m here ro help u out
let us suppose a equation
a.x(pow n) + b.x(pow n-1)+c.x(n-2)+d.x(n-3)+c=0
then
sum of roots taken one at a time= -coeff of x(pow n-1)/coeff of x(pow n)
sum of roots taken two at a time=coeff of x(n-2)/coeff of x(pow n)
sum of roots taken three at a time= -coeff of x(n-3)/coeff of x(pow n)
u notice the pattern?alternate signs?
ok
now product of roots=(+or-)coeff of constant term/coeff of x(pow n)
sign would be positive for an even degree equation and negative for odd degree equation.
i thing i cleared ur doubts
say thanks!!!!!!!!!!!!!!!!! |
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