Question

If (x²-1) is a factor of ax⁴+bx³+cx²+dx+e ,s
Show that a+c+e=b+d

Answer 1

(x²-1) is a factor of ax⁴+bx³ +cx² +dx +e.
so, (x-1) and (x +1) are factor of ax⁴+bx³ +cx² +dx +e
so, 1 and -1 are the zeros of ax⁴+bx³ +cx² +dx +e.

    put x =  -1 in expression,
a(-1)⁴+b(-1)³+c(-1)²+d(-1)+e = 0
a -b + c -d + e =0
a + c + e = b +d 
      Hence proved/