Question

ax^3+bx^2-5x-2可被x+1和x-2整除 求a、b值

Answer 1

ax^3+bx^2-5x-2可被x+1整除,说明ax^3+bx^2-5x-2有因子x+1,所以当x = -1时ax^3+bx^2-5x-2=0,

即-a + b + 5 - 2=0,

同理,当x = 2时ax^3+bx^2-5x-2=0,即8a + 4b -10 -2 =0,

整理

a - b = 3

2a + b = 3

解得a = 2,b = -1