CAT 2019 Question Paper | Quants Slot 2

CAT Questions

Quadratic Equations is a topic that falls in the trickier topics under the CAT Syllabus and hence needs attention from your end. You can ace questions of this sort easily by practicing CAT previous year paper questions. They'll also help you have a grip over the difficulty level of questions that you can expect in the upcoming CAT exam so that you do not waste your time in practicing harder questions. Level up your online CAT preparation by solving these questions, starting right now with this question taken from CAT 2019 Question Paper.

Question 25 : 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?

1. 3721
2. 549
3. 361
4. 427

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Video Explanation

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Explanatory Answer

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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The question is "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? "

Hence, the answer is 549

Choice B is the correct answer.