The quadratic equation x^2 + bx + c = 0 | Quantitative Aptitude – Quadratic Equation

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The question below is from previous year CAT question from CAT 2019 exam comes from Quadratic Equation: The quadratic equation x^2 + bx + c = 0. Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

CAT 2019 – Slot -2 - Question 2 - The quadratic equation x^2 + bx + c = 0

Q. 2: 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?

1. 3721

2. 549

3. 361

4. 427

Show Answer

Sum of roots = -b

4a + 3a = -b

b^2 = 49a^2

similarly product of roots = c

or 12a^2 = c

thus b^2 + c = 49a^2 + 12a^2 = 61a^2

as a is integers so b^2 + c can be 61, 61*4 , 61*9 ….so on

so option b ) 549 that is 61*9 is correct.

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