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16 May 2018, 04:43
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
81% (01:17) correct
19%
(01:00)
wrong
based on 31
sessions
History
Date
Time
Result
Not Attempted Yet
Which equation below has roots of 4 and \(\frac{1}{2}\)?
A. \(4x^2 -9x + 2 =0\)
B. \(2x^2 - 9x + 4 = 0\)
C. \(2x^3 - 9x^2 + 4x = 0\)
D. \(2x^2 + 9x + 4 = 0\)
E. \(x^2 - 2x + \frac{1}{2} = 0\)
A. \(4x^2 -9x + 2 =0\)
B. \(2x^2 - 9x + 4 = 0\)
C. \(2x^3 - 9x^2 + 4x = 0\)
D. \(2x^2 + 9x + 4 = 0\)
E. \(x^2 - 2x + \frac{1}{2} = 0\)
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16 May 2018, 04:50
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Solution
Given:
• The roots of the equation, that is to be determined, are 4 and 1/2
To find:
• What is the equation with roots 4 and \(\frac{1}{2}\)
Approach and Working:
• As 4 is a root of the equation, we can say (x – 4) = 0
• Similarly, \(\frac{1}{2}\) is a root of the equation, we can say (x – \(\frac{1}{2}\)) = 0 or, (2x – 1) = 0
• Multiplying both, we get:
- o (x – 4) (2x – 1) = 0
Or, 2\(x^2\) – 9x + 4 = 0
Hence, the correct answer is option B.
Answer: B
18 May 2018, 11:18
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Bunuel
If an equation has roots of 4 and 1/2, then it can be factored as (x - 4)(2x - 1) = 0. If we expand it, we will have 2x^2 - x - 8x + 4 = 0, i.e., 2x^2 - 9x + 4 = 0.
(Note: Choice C could also be the answer; notice that 2x^3 - 9x2 + 4x = 0 → x(2x^2 - 9x + 4) = 0 → x(x - 4)(2x - 1) = 0. So choice C also has 4 and 1/2 as roots (in addition, it has has 0 as a root). Though we think the answer should be B, the wording of the problem should be: “Which equation below has roots of ONLY 4 and 1/2?” Then we can avoid any ambiguity between choices B and C.)
Answer: B
