Question

If x²-1 Is a factor of ax⁴+bx³+cx²+dx+e,then show that ,a+c+e=b+d=0 ?

Answer 1

x^2-1 is a factor for

ax^4+bx^3+cx^2+d^x+e

show that:

1) a+b+c+d+e=0

X^2-1 is a factor means that x^2-1 zero are the function's zeros too.

x^2-1=0

==> x1= 1 x2=-1

Now by substituting in the function:

x=1 ==> a(1)+b(1)+c(1)+d(1)+e=0

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

2) a+c+e = b+d

To prove that we need to substitute with x=-1 (the other root)

==> a(-1)^4+b(-1)^3+c(-1)^2+d(-1)+e=0

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

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