Question

If x² − 1 is a factor of ax⁴ + bx³ + cx² + dx + e, then

(a) a + c + e = b + d

(b) a + b +e = c + d

(c) a + b + c = d + e

(d) b + c + d = a + e

Answer 1

Asis a factor of polynomial

Therefore,

And

f(1) = 0

$$\begin{gathered} a{\left(1\right)}^4+b{\left(1\right)}^3+c{\left(1\right)}^2+d\left(1\right)+e=0 \\ \Rightarrow a+b+c+d+e=0 \end{gathered}$$

And

Hence,

The correct option is (a).