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Chisinau City MO
1949-56 Chisinau City MO
17
17
Part of
1949-56 Chisinau City MO
Problems
(1)
Chisinau MO p17 1949-56 VIII-IX x^2+px+q+(x+a)(2x+p)=0 has real roots for any a
Source:
3/15/2021
Prove that if the roots of the equation
x
2
+
p
x
+
q
=
0
x^2 + px + q = 0
x
2
+
p
x
+
q
=
0
are real, then for any real number
a
a
a
the roots of the equation
x
2
+
p
x
+
q
+
(
x
+
a
)
(
2
x
+
p
)
=
0
x^2 + px + q + (x + a) (2x + p) = 0
x
2
+
p
x
+
q
+
(
x
+
a
)
(
2
x
+
p
)
=
0
are also real.
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trinomial
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