Quantitative Aptitude – Algebra – Quadratic Equation


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

Q. 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
Answer: 549

Solution: 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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