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  • If p is a prime and both roots of x^2+px-444p=0 are integers then p is equal to

If p is a prime and both roots of x^2+px-444p=0 are integers then p is equal to

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Solution :   Discriminant ,   D=p(p+1776) must be perfect square.

          Rightarrow         p+1776  and hence  1776 must be a multiple  of p

       Now ,   1776=2^4cdot 3cdot 37,  if follows that p=2,3hspace0.2cmor hspace0.2cm37.

      But   D is perfect square for  p=37 only

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Deependra Verma

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