第2个当方程有两个不相等的实数解且不为0±1data=a的平方-16>0就下面这个这两个为什么要1+1+4不=0和1-1 1+4不=0吗？---**Extraction Content:** **Problem Title:** 【题目】 **Problem Stem:** 定义[A]表示集合A中元素的个数，A⊗B=∣[A]−[B]∣. 已知集合M={1,2},集合A是由集合M的子集构成, 集合B={x∣x(x^2-ax+4)=0},若A⊗B=1,则a的取值范围是( ) **Definition of Operation:** [A]表示集合A中元素的个数 A⊗B=∣[A]−[B]∣ **Set Definitions:** 集合M={1,2} 集合A是由集合M的子集构成 集合B={x∣x(x^2-ax+4)=0} **Condition:** A⊗B=1 **Question:** 则a的取值范围是( ) **Options:** A. {a∣-40, 即a>4或a<-4. 此时[B]=3. ③ 当方程有两个相等实根且不为0时, Δ = a^2-16=0, 即a=±4. 此时[B]=2. 排除a=0, ±1 (Written next to the options) 故a≠±4且a≠±5 (Written next to option D, with a checkmark on D) **(Note on the handwritten notes: The steps analyze the number of roots of x(x^2-ax+4)=0, which determines [B]. It correctly identifies the conditions for [B]=1, 2, and 3 based on the discriminant of the quadratic part. The initial statement "[B]=3或5" seems extraneous or incorrect based on the subsequent analysis. The "排除a=0, ±1" and "故a≠±4且a≠±5" notes suggest exclusions that do not directly follow from the initial derivation and likely relate to the intended answer or a separate line of reasoning not fully documented.)** **Chart/Diagram Description:** The image does not contain charts or diagrams in the typical sense (like statistical charts, flowcharts, geometric figures). It primarily contains text and mathematical expressions/equations arranged vertically, with handwritten annotations and calculations beside them. There are no axes, points, lines, or shapes other than the text characters themselves.