let A,B are the roots of this equation then
A+B = -p      ,    AB = q
if one root is 2+31/2 then other can be 2-31/2 or 31/2-2
 case 1) (A,B) = (2+roo3 , 2-root3)                                 case2) (A,B) = (root3-2) , (root3+2)
          A+B = 4 = -P                                                                       A+B = 2root3 = -p
      AB = 4-3 = 1 = q                                                                      AB = -1   = q
now we have two odered pairs for (p,q)
p,q ={ (-4,1) , (-2root3,-1) }
						

							
Dear student,
Sum of the roots=-p
Product =q
Now one of the roots is given 2+root3
You can easily finc the value of p and q











































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if p n q are real no.s then if 2+sqrt3 is root then 2-sqrt3 has to b d root as well.
thr4 p=-4    q=1