(a2+b2)x2−2(ac+bd)x+c2+2=0
Comparing with Ax2+Bx+c=0
A=(a2+b2)
B=−2(ac+bd)
C=c2+d2
b2−4ac
=4(ac+bd)2−4(a2+b2)(c2+d2)
=4(a2c2+b2d2+2abcd)−4(a2c2+a2d2+b2c2+b2d2)
=8abcd−4(a2d2+b2c2)
=−4[(ad)2+(bc)2−2abcd]
=−4[(ad−bc)2]
Roots are equal if ad = bc