let A,B are the roots of this equation then

A+B = -p      ,    AB = q

if one root is 2+3^1/2 then other can be 2-3^1/2 or 3^1/2-2

 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

Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.

All the best.

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

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