if the equation(a^2+b^2)x^2-2(ac+bd)x+c^2+d^2=0 has equal roots,then
a) ad=bc
b) ab=cb
c) ad= square root of bc
d) ab= square root of cd
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1
Answer
Correct option is
B
ad=bc
(a
2
+b
2
)x
2
−2(ac+bd)x+(c
2
+d
2
)=0 has equal roots.
Therefore, discriminant =0
Thus [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
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