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India IMO Training Camp
2012 India IMO Training Camp
2
Prove that quadratic equation has real roots.
Prove that quadratic equation has real roots.
Source:
July 17, 2012
quadratics
Problem Statement
Let
a
≥
b
a\ge b
a
≥
b
and
c
≥
d
c\ge d
c
≥
d
be real numbers. Prove that the equation
(
x
+
a
)
(
x
+
d
)
+
(
x
+
b
)
(
x
+
c
)
=
0
(x+a)(x+d)+(x+b)(x+c)=0
(
x
+
a
)
(
x
+
d
)
+
(
x
+
b
)
(
x
+
c
)
=
0
has real roots.
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