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If x2 +  Px – 444P = 0 has integral roots (where P is a prime number) then the value of  
    Correct answer is '4'. Can you explain this answer?
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    If x2 + Px 444P = 0 has integral roots (where P is a prime number) th...
     The equatio n x2 + Px  – 444P = 0 has integral roots.  
    Since P = 2 does not give the integral roots.  
    ⇒  D must be perfect square of an odd integer.  
    i.e.  D2 = P(P + 1776) since perfect square.  
    ⇒  P + 1776 must be multiple of P   
    ⇒  1776 must be a multiple of P  
    Now, 1776 = 24.3.37 when;   P = 2 or 3 or 37.  
    (i) P = 2 then P(P + 1776) = 2(2 + 1776) = 3556, not a perfect square.  
    (ii) P = 3 then P(P + 1776) = 3(3 + 1776) = 5337, not a perfect square.  
    (iii) P = 37 then P(P + 1776) = 37(37 + 1776) = 372.72 which is odd.  
    ∴  P = 37  
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