Question

求出P的值 (2+p)x + 6px^2 + p^2 -4p 可以被 x-1整除 但 x+1不行

Answer 1

f(x) = (2+p)x + 6px^2 + p^2 -4p

f(x)能被x-1整除

即f(x)=(x-1)p(x)

所以f(1)=0

(2 + p) + 6p + p² - 4p = 0

p = -1 或 -2

当p=-1

f(x) = -6x² + x + 5 = -(x - 1)(6x + 5)

当p=-2

f(x) = -12x² + 12 = -12(x + 1)(x - 1),能被x+1整除

所以只有p = -1满足