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

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

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

Now ,   $1776=2^{4}\cdot 3\cdot 37,$  if follows that $p=2,3\hspace{0.2cm}or \hspace{0.2cm}37.$

But   $D$ is perfect square for  $p=37$ only

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