If the sum of the roots of the equation 1/(x+a)+1/(x+b)=1/c is zero, prove that the product of the roots is - 1/2(a2+b2)
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Answer:
Correct option is
D
−
2
(a
2
+b
2
)
Simplifying we get
x
2
+(a+b)x+ab
2x+a+b
=
c
1
⇒x
2
+x(a+b)+ab=2cx+bc+ac
⇒x
2
+x(a+b−2c)+ab−bc−ac=0
Hence it is given that the sum of roots is 0.
Now, we get
a+b−2c=0
c=
2
a+b
Therefore, product of roots is
ab−(a+b)c
=ab−
2
(a+b)
2
=
2
2ab−(a+b)
2
=
2
−(a
2
+b
2
)
Hence,answer is
2
−(a
2
+b
2
)
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