Question

If the equations [tex] x^{2} -x-p=0 & x^{2} -2px -12 =0 have a common root then that root is

Answer 1

if a_1x^2 + b_1x+c1=0 and a_2x^2 + b_2x+c2=0 are having a common root then
root  = (b1c2 -b2c1) / ( c1a2 - a1c2 )
or
root = ( c1a2 - a1c2 ) / (a1b2 - a2b1)


In this problem the root is
(12 - 2P^2)/(12-P)
or
(12-P)/(1-2P)