Quantitative Aptitude – Quadratic Equation – Let m and n be positive integers, If x^2


Slot – 3 – Quantitative Aptitude – Quadratic Equation – Let m and n be positive integers, If x^2


Q. Let m and n be positive integers, If x^2 + mx + 2n = 0 and x^2 + 2nx + m = 0 have real roots, then the smallest possible value of m + n is?
  1. 7
  2. 5
  3. 6
  4. 8
Answer: 6

Solution :
Both have real roots so , D > = 0 for both quadratic equations .
Which means m^2- 8n ≥0 and 4n^2- 4m≥0
m^2≥8n and n^2≥m or n^4≥m^2 which means n^4 >8n or n>2
So minimum value of n = 3 and that of m =5
Thus m+n = 3+5=8


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