Problem: At the midpoint of line segment AB which is p units long, a perpendicular MR is erected with length q units. An arc is described from R with a radius equal to 21​AB, meeting AB at T. Then AT and TB are the roots of:
Answer Choices:
A. x2+px+q2=0
B. x2−px+q2=0
C. x2+px−q2=0
D. x2−px−q2=0
E. x2−px+q=0
Solution:
Since MT=2p2−4q2​​,AT=AM+MT=2p+p2−4q2​​ and TB=AB−AT=2p−p2−4q2​​. The required equation is, therefore, x2−px+q2=0.
