Find the value of a and b if (x - 1) and (x + 1) are factors of x⁴ + ax³ - 3x² + 2x + b = ?

Solution(By Examveda Team)

If (x - 1) and (x + 1) are the factors y equation then,
$$\eqalign{ & x - 1 = 0 \cr & x = 1 \cr & \Rightarrow {\text{Put }}x = 1{\text{, we get }} \cr & 1 + a - 3 + 2 + b = 0 \cr & a + b = 0\,.....(i) \cr & \Rightarrow x + 1 = 0 \cr & \Rightarrow x = - 1 \cr & {\text{Put }}x = - 1,{\text{we get }} \cr & 1 - a - 3 - 2 + b = 0 \cr & b - a = 4\,.....(ii) \cr & {\text{After solving (i) & (ii),}} \cr & {\text{We get }} \cr & a = - 2,{\text{ }}b = 2 \cr} $$