If (x - 1) and (x + 3) are the factors of x² + k₁x + k₂ then-

$$\eqalign{ & \therefore {\text{When}}\left( {x - 1} \right) = 0 \cr & x = 1 \cr & {x^2} + {k_1}x + {k_2}{\text{ }} = 0 \cr & \Rightarrow 1 + {k_1} + {k_2}{\text{ }} = 0 \cr & \Rightarrow {k_1} + {k_2} = - 1\,.......(i) \cr & {\text{When}}\left( {x + 3} \right) = 0 \cr & x = - 3 \cr & 9 - 3{k_1} + {k_2}{\text{ }} = 0 \cr & \Rightarrow - 3{k_1} + {k_2}{\text{ }} = - 9\,.......(ii) \cr & {\text{From equation (i) and (ii)}} \cr & {k_1} = 2,\,\,\,\,\,\,{\text{ }}{k_2} = - 3 \cr} $$