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22 May 2020, 06:57
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Bunuel
4a+3a=-b/a, b=-7a
4a*3a=c/a, c=12a^2
b^2+c=49a^2+12a^2=61a^2
3721=61a^2, a=√61≠integer
549/61=integer, a=√9=integer
ans (C)
21 May 2023, 07:54
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Given: The quadratic equation \(x^2 + bx + c = 0\) has two roots \(4a\) and \(3a\), where \(a\) is an integer.
Asked: Which of the following is a possible value of \(b^2 + c\) ?
Sum of roots = 4a + 3a = 7a = -b
Product of roots = 4a * 3a = 12a^2 = c
b^2 + c = 49a^2 + 12a^2 = 61a^2
A. 3721 = 61*61: Since 61*61 is NOT of the form 61a^2: Incorrect
B. 550 : Is not a multiple of 61: Incorrect
C. 549 = 61*3^2 : Is of the form 61a^2: Correct
D. 427 = 61*7 : Is NOT of the form 61a^2: Incorrect
E. 361 : Is not a multiple of 61: Incorrect
IMO C
Asked: Which of the following is a possible value of \(b^2 + c\) ?
Sum of roots = 4a + 3a = 7a = -b
Product of roots = 4a * 3a = 12a^2 = c
b^2 + c = 49a^2 + 12a^2 = 61a^2
A. 3721 = 61*61: Since 61*61 is NOT of the form 61a^2: Incorrect
B. 550 : Is not a multiple of 61: Incorrect
C. 549 = 61*3^2 : Is of the form 61a^2: Correct
D. 427 = 61*7 : Is NOT of the form 61a^2: Incorrect
E. 361 : Is not a multiple of 61: Incorrect
IMO C
04 Sep 2025, 12:21
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