Tap roots are common in

MC curve is common to both :

Suppose two quadratic equations a_(1)x^(2)+b_(1)x+c_(1)=0 and a_(2)x^(2)+b_(2)x+c_(2)=0 have a common root alpha , then a_(1)alpha^(2)+b_(1)alpha+c_(1)=0 " " …..(1) and a_(2)alpha^(2)+b_(2)alpha+c_(2)=0 " " ……(2) Eliminating alpha using crose - multiplication method gives us the condition for a common root Solving two equations simultaneously, the common root can be obtained. Now, consider three quadratic equations, x^(2)-2r p_(r )x+r=0, r=1, 2, 3 given that each pair has exactly one root common. The common root between the equations obtained by r = 1 and r = 3 is