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The quadratic equation x^2 + bx + c = 0 has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of b^2 + c?
The quadratic equation x2 + bx + c = 0 has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of b2 + c?
This question was asked in CAT-2019 and options were
- 3721
- 549
- 361
- 427
Thanks in advance
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Given quadratic equation is x2 + bx + c = 0
Sum of roots = -b
-b = 4a + 3a
-b = 7a
Product of the roots = c
c = 4a x 3a
c = 12a2
b2 = 49a2 and c =12a2
b2 + c = 49a2 + 12a2
b2 + c = 61 a2
Our answer must be a multiple of 61, which should be a perfect square
Going through the options,
549 = 61 x 9
549 = 61 x 32
Thus, possible value of b2 + c = 549
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