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Swedish Mathematical Competition
1988 Swedish Mathematical Competition
4
4
Part of
1988 Swedish Mathematical Competition
Problems
(1)
no fo real roots of P'(x)^2 -2P(x)P''(x) = 0 if P has 3 real distinct
Source: 1988 Swedish Mathematical Competition p4
3/28/2021
A polynomial
P
(
x
)
P(x)
P
(
x
)
of degree
3
3
3
has three distinct real roots. Find the number of real roots of the equation
P
′
(
x
)
2
−
2
P
(
x
)
P
′
′
(
x
)
=
0
P'(x)^2 -2P(x)P''(x) = 0
P
′
(
x
)
2
−
2
P
(
x
)
P
′′
(
x
)
=
0
.
polynomial
algebra
analysis