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 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?

- 3721
- 549
- 361
- 427

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Given quadratic equation is x^{2} + bx + c = 0

Sum of roots = -b

-b = 4a + 3a

-b = 7a

Product of the roots = c

c = 4a x 3a

c = 12a^{2}

b^{2} = 49a^{2} and c =12a^{2}

b^{2 }+^{ }c = 49a^{2 }+ 12a^{2}

b^{2 }+^{ }c = 61 a^{2}

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 3^{2}

Thus, possible value of b^{2 }+^{ }c = 549

The question is **"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? " **

**Choice B** is the correct answer.

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