maths question:polynomials plz help..

[saadiyah]

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.

[astarmathsandphysics]

Quotient is x2-1 remainder is x solutions are -+1

[saadiyah]

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?

[astarmathsandphysics]

When i get access to a pc shortly.

[astarmathsandphysics]

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

[saadiyah]

thx a lot!

[astarmathsandphysics]

No probs.