Question

For which condition the quadratic equation (a2+b2)x2-2(ac+bd)x+(c+d)=0 has equal roots.

Answer 1

Answer:

[2(ac+bd)]

2

+4(a

2

+b

2

)(c

2

+d

2

)

⇒a

2

c

2

+b

2

d

2

+2ac.bd=a

2

c

2

+a

2

d

2

+b

2

c

2

+b

2

d

2

⇒(ad−bc)

2

=0$

⇒ad−bc=0

⇒ad=bc