回答：
3根是 #x = -3 / 2,1,3 / 2#
注意我找不到长除法符号所以我将在它的位置使用平方根符号。
说明：
#F（X）= 4×^ 3-4倍^ 2-9x + 9#
#F（1）= 4 * 1 ^ 3-4 * 1 ^ 2-9 * 1 + 9 = 4-4-9 + 9 = 0#
这意味着x = 1是根和 #（X-1）# 是这个多项式的一个因素。
我们需要找到其他因素，我们通过将f（x）除以得到 #（X-1）# 找到其他因素。
#{4倍^ 3-4倍^ 2-9x + 9} / {X-1}#
#（X-1）的sqrt（4倍^ 3-4倍^ 2-9x + 9）#
以来 #（X * 4倍^ 2）= 4×^ 3# 我们得到 #4X ^ 2# 作为因素的一个术语
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #4X ^ 2#
#（X-1）的sqrt（4倍^ 3-4倍^ 2-9x + 9）#
我们需要找到其余部分以找到还需要找到的东西。
我们的确是 #4倍^ 2 *（X-1）= 4×^ 3-4倍^ 2#
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #4X ^ 2#
#（X-1）的sqrt（4倍^ 3-4倍^ 2-9x + 9）#
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #4倍^ 3-4倍^ 2#
我们减去这个得到0
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #4X ^ 2#
#（X-1）的sqrt（4倍^ 3-4倍^ 2-9x + 9）#
# # # # # # # # # # # # # # # # # # # # # # # # #ul { - （4x ^ 3-4x ^ 2）}#
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # ## # # # #0X ^ 3-0x ^ 2#
这个零意味着我们没有线性项，并且下一个条款。
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #4x ^ 2 + 0 x#
#（X-1）的sqrt（4倍^ 3-4倍^ 2-9x + 9）#
# # # # # # # # # # # # # # # # # # # # # # # # #ul { - （4x ^ 3-4x ^ 2）}#
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #0X ^ 3-0x ^ 2# #-9x + 9#
#X * -9 = -9x# 所以下一学期是 #-9#
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #4x ^ 2 + 0 x -9#
#（X-1）的sqrt（4倍^ 3-4倍^ 2-9x + 9）#
# # # # # # # # # # # # # # # # # # # # # # # # #ul { - （4x ^ 3-4x ^ 2）}#
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #0X ^ 3-0x ^ 2# #-9x + 9#
#-9 *（x-1）= - 9x + 9#
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #4x ^ 2 + 0 x -9#
#（X-1）的sqrt（4倍^ 3-4倍^ 2-9x + 9）#
# # # # # # # # # # # # # # # # # # # # # # # # #ul { - （4x ^ 3-4x ^ 2）}#
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #0X ^ 3-0x ^ 2# #-9x + 9#
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #ul { - （ - 9x + 9）}#
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #4x ^ 2 + 0 x -9#
#（X-1）的sqrt（4倍^ 3-4倍^ 2-9x + 9）#
# # # # # # # # # # # # # # # # # # # # # # # # #ul { - （4x ^ 3-4x ^ 2）}#
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #0X ^ 3-0x ^ 2# #-9x + 9#
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #ul { - （ - 9x + 9）}#
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #0#
所以 #（x-1）（4x ^ 2 -9）# 没有提醒（您可以通过扩展来检查）。我们需要完全考虑这一点。
#（4x ^ 2 -9）# 是因子与方格的差异 #（2X-3）*（2×+ 3）#
我们有 #（x-1）*（2x-3）*（2x + 3）= 0#
#2X-3 = 0# 给了我们一个根源 #X = 3/2# 和 #2X + 3 = 0# 给了我们一个根源 #X = -3 / 2#
根源是 #x = -3 / 2,1,3 / 2#
