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Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: saadiyah on September 16, 2009, 06:30:54 pm

Title: maths question:polynomials plz help..
Post by: saadiyah on September 16, 2009, 06:30:54 pm
let f(x)= x4 + (a-1)x2 + x - a, where a is a +ve constant.

find 1. the quotient and remainder when f(x) is divided by (x2 + a).
      2. hence find the real roots of the eqn f(x) = x.
Title: Re: maths question:polynomials plz help..
Post by: astarmathsandphysics on September 16, 2009, 10:27:33 pm
Quotient is x2-1 remainder is x solutions are -+1
Title: Re: maths question:polynomials plz help..
Post by: saadiyah on September 17, 2009, 07:24:43 am
thx astar.actually it's the answer but i'm so dumb tht i can't understand how to get tht. would u send me the method plz?
Title: Re: maths question:polynomials plz help..
Post by: astarmathsandphysics on September 17, 2009, 07:48:13 am
When i get access to a pc shortly.
Title: Re: maths question:polynomials plz help..
Post by: astarmathsandphysics on September 17, 2009, 10:05:51 am
Quote from: saadiyah on September 16, 2009, 06:30:54 pm
let f(x)= x4 + (a-1)x2 + x - a, where a is a +ve constant.

find 1. the quotient and remainder when f(x) is divided by (x2 + a).
      2. hence find the real roots of the eqn f(x) = x.

x4 + (a-1)x2 + x - a=((x2 + a))(x2+cx+d)+fx+e
                                                                   =x4+cx3+x2(d+a)+x(ac+f)+ad+e

from which c=0, a-1=d+a so d=-1 ,and, f=1,-a=ad+e=-a+e so a is arbitrary and e=0

hence qutient is x2-1 and remaider is x
2. f(x)=x s0 x4 + (a-1)x2 + x - a=x so x4 + (a-1)x2- a=0 so(x2+a)(x2-1)=0 the first factor has no roots but the roots of the second are \pm 1

Title: Re: maths question:polynomials plz help..
Post by: saadiyah on September 17, 2009, 03:32:44 pm
thx a lot! :)
Title: Re: maths question:polynomials plz help..
Post by: astarmathsandphysics on September 17, 2009, 05:10:57 pm
No probs.