Question

if x^2 -1 is a factor of ax^3+bx^2+cx+d. Show that a+c = 0​

Answer 1

Answer:

let p(x) =x^3+bx^2+cx+d

(x^2-1)is a factor

x^2-1=0

x^2=1

x=+1 or -1

p(1)=a×1+b×1+c×1+d=0

a+b+c+d=0

a+c=-b-d...(1)

p(-1)=-a+b-c+d=0

a+c=b+d...(2)

adding (1) and (2) we get,

2(a+c)=0

a+c=0

hence proved

hope it helps.