In a triangle ABC,  C=  π2  and tanA2,tanB2  are the roots of the equation px2+qx+r=0,  p≠0 then

The given quadratic equation is px2+qx+r=0 tanA2,tanB2  are the given roots equationSum of the roots tanA2+tanB2=−qpProduct of the roots tanA2.tanB2=rpGiven C=π2⇒  A+B  =π  −C=π  −  π2=  π2⇒    A2  +B2  =  π2  Applying tan on both sides⇒  tan  (A2+B2)=1      (∵tanπ2=1)⇒    tanA2+tanB21−tanA2tanB2=1      (∵tan(A+B)=tanA+tanB1−tanAtanB)⇒  −qp1−rp=1⇒  −qp−r=1  ⇒ p+q=r.