Question

If (xsquare -1)is a factor of ax4+bxcube+cxsquar+dx+e, show that a+c+c=b+d=0.​

Answer 1

Answer:

Since ( x^2-1)is a factor of ax^4+bx^3+cx^2+dx+e so (x^2-1) satisfies it.

It means (x+1)(x-1) satisfies it.

=> x=1 or x= -1 satisfy it

So for x=1 => a+b+c+d+e+f =0 => a + c + e = -(b + d) --------- (1)

and for x= -1

=> a-b+c-d+e = 0

=> a+ c + e = b + d ------ (2)

=> b + d = -(b + d)

=> b + d = 0 ---------(3)