Question

( x^{2}-1 ) is a falce of ( cos (x)=a x^{4}+b x^{3} )
( +c x^{2}+d x+e ) men ( x^{2}-1 ) munt
Thus at ( x=1, p(x) ), becmes, ( P(1)=0 ) ( P(1)=a+b+c+d+e=0 quad-0 )
Also ( , quad P(-1)=0 )
( p(-1)=a-b+c-d+e=0 )
Adding 0 and ( (2, ), we get, ( a+b+c+x+e+a-b+c-d+e=0 )
( a+c+e+a+c+e=0 )
( 2(a+c+c)=0 )
( Rightarrow quad a+c+e=0 )
Subleact
(1) and 2 , we get ( a+b+c+d+e-a+b-c+d-e=0 )
( b+d+b+d=0 )
( 2(b+d)=0 )
( b+d=0 )
( Rightarrow quad a+c+c=b+d=0 )

# 18/ (x-1) is a factor of ax +bx+cx+dx*e Show that a+cée bd 0. is diuisible by x2-3x+2.

Solution