The smallest possible natural number n , for which the equation x 2 - n x + 2014 = 0 has integral roots, is

Question

The smallest possible natural number n , for which the equation x 2 - n x + 2014 = 0 has integral roots, is,

MARKS App · Accepted Answer

In x 2 - n x + 2014 = 0 α + β = n and α β = 2014 Now, α β = 2014 = 1 × 2014 or - 1 × - 2014 = 2 × 1007 or - 2 × - 1007 = 19 × 106 or - 19 × - 106 = 38 × 53 or - 38 × - 53 For least possible value, n = α + β = 38 + 53 = 91

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