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drakehikcs
Joined: 13 Jul 2019
Last visit: 25 Jan 2021
Posts: 3
Given Kudos: 1
Location: United States
Schools: INSEAD Sept'21 Intake (A)
03 Aug 2020, 12:16
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
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Question Stats:
68% (01:56) correct
32%
(02:11)
wrong
based on 241
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Which of the following describes all the values of x such that 3x^2 − 5x − 12 > 0?
A. -4/3 < x < 3
B. x > 3
C. x <
D. x > 3 or x < −4
E. x > 3 or x <-4/3
A. -4/3 < x < 3
B. x > 3
C. x <
D. x > 3 or x < −4
E. x > 3 or x <-4/3
3x2 − 5x − 12 = (x − 3)(3x + 4). So the inequality 3x2 − 5x − 12 > 0 can be rewritten (x − 3)(3x + 4) > 0. For this equation, why do you test for both positive and negative values?
I understand x>3, and x>-4/3, which is the single requirement that x>3, but then considering the possibility that x − 3 < 0 and 3x + 4 < 0. If x − 3 < 0, is that general practice? Can you help me understand this?
I understand x>3, and x>-4/3, which is the single requirement that x>3, but then considering the possibility that x − 3 < 0 and 3x + 4 < 0. If x − 3 < 0, is that general practice? Can you help me understand this?
03 Aug 2020, 12:33
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drakehikcs
We have: 3x^2 − 5x − 12 > 0
=> (x − 3)(3x + 4) > 0
Consider the function: y = (x − 3)(3x + 4)
The roots of y = 0 are: x = 3 or x = -4/3
The graph of this is presented below:
Attachment:
1.JPG [ 19.25 KiB | Viewed 3860 times ]
Since we need (x − 3)(3x + 4) > 0, i.e. y > 0, we look at the positive part of y
The y-values are positive when x > 3 or x < -4/3 - hence, this is the solution
Alternative approach:
Case 1: Positive * Positive > 0
Thus: x - 3 > 0 and x + 4/3 > 0 => x > 3 and x > -4/3 => x > 3 (common region)
Case 2: Negative * Negative > 0
Thus: x - 3 < 0 and x + 4/3 < 0 => x < 3 and x < -4/3 => x < -4/3 (common region)
Thus, the solution: x > 3 or x < -4/3
Hope this helps!
04 Aug 2020, 03:03
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drakehikcs
Solution
- • \(3x^2 -5x – 12 > 0\)
- o \( ⟹ 3x^2 -9x + 4x – 12 > 0\)
o \( ⟹ (x -3)(3x + 4) > 0\)
• Let’s draw the number line diagram as shown below:
• Thus, from the above, number line diagram, \(x < -\frac{4}{3}\) or \(x > 3\)
Thus, the correct answer is Option E.
