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Mathematics
Mathematics
Problem
If
α
\alpha
α
is a root of the equation
a
x
2
+
b
x
+
c
=
0
ax^2 + bx + c = 0
a
x
2
+
b
x
+
c
=
0
and
β
\beta
β
is a root of the equation
−
a
x
2
+
b
x
+
c
=
0
-ax^2 + bx + c = 0
−
a
x
2
+
b
x
+
c
=
0
, then prove that there will be a root of the equation
a
2
x
2
+
b
x
+
c
=
0
\frac{a}{2}x^2 + bx + c = 0
2
a
x
2
+
b
x
+
c
=
0
lying between
α
\alpha
α
and
β
\beta
β
.
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