Many students arrive at the last step with something like the following.
(1) (x – a)(x – b) ≤ 0
(2) (x – a)(x – b) < 0
(3) (x –
a)(x – b) ≥ 0
(4) (x – a)(x – b) > 0
Method 1:
Now we assume a < b
Now we assume a < b
Answer for (1) : a ≤ x ≤ b
Answer for (2) : a < x < b
Answer for (3) : x ≤ a or x ≥ b
Answer for (4) : x < a or x > b
Answer for (4) : x < a or x > b
Method 2 is to draw a graph. Here is an example.
Turn into (x – a)(x – b) form
Answer : D
For this type of question, you may assign real values for a and b. For instance, a = -2, b = -1.
It is easily seen that D is the answer.
If the condition is just a < b, you have to consider all the probabilities.
(1) Both positive
(2) Both negative
(3.1) One negative, one positive (a = -1, b = 2)
(3.2) One negative, one positive (a = -2, b = 1)
Answer : E
Answer : D
Draw a picture and find the intersection part.
空心代表 >/<
實心代表 ≥/≤
Answer : D
For this type of question, you may assign real values for a and b. For instance, a = -2, b = -1.
It is easily seen that D is the answer.
If the condition is just a < b, you have to consider all the probabilities.
(1) Both positive
(2) Both negative
(3.1) One negative, one positive (a = -1, b = 2)
(3.2) One negative, one positive (a = -2, b = 1)
Answer : E
6x2–7x–20
≤ 0
(2x –5)(3x
+ 4) ≤
0
(x–5/2)(x
+ 4/3) ≤
0
-4/3 ≤ x ≤ 5/2
Hence, we have -1, 0, 1, 2.
Answer : D
Draw a picture and find the intersection part.
空心代表 >/<
實心代表 ≥/≤
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