MathDB
Problems
Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2013 India PRMO
16
16
Part of
2013 India PRMO
Problems
(1)
2013 preRMO p16, common root, x^3 - 3x + b=0, x^2 + bx -3=0
Source:
8/8/2019
Let
f
(
x
)
=
x
3
−
3
x
+
b
f(x) = x^3 - 3x + b
f
(
x
)
=
x
3
−
3
x
+
b
and
g
(
x
)
=
x
2
+
b
x
−
3
g(x) = x^2 + bx -3
g
(
x
)
=
x
2
+
b
x
−
3
, where
b
b
b
is a real number. What is the sum of all possible values of
b
b
b
for which the equations
f
(
x
)
f(x)
f
(
x
)
= 0 and
g
(
x
)
=
0
g(x) = 0
g
(
x
)
=
0
have a common root?
Sum
algebra
Root