if the roots of the equation ax²+bx+c=0,are two consecutive integers then prove that,b²-a²=4ac
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Answer:
Roots for the given equation are
−
b
−
k
2
a
and
−
b
+
k
2
a
,where
k
=
√
(
b
2
−
4
a
c
)
So,if these two roots are consecutive integers we can write,
−
b
−
k
2
a
+1=
−
b
+
k
2
a
Solving this one we get,
2
⋅
√
b
2
−
4
a
c
2
⋅
a
=
1
Or,
b
2
−
4
a
c
=
a
2
Or,
b
2
−
a
2
=
4
a
c
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