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2013 Saudi Arabia Pre-TST
2.2
2.2
Part of
2013 Saudi Arabia Pre-TST
Problems
(1)
max of (a - b)(2a - b)}/a(a - b + c) when ax^2 + bx + c = 0 has roots in [0, 1]
Source: 2013 Saudi Arabia Pre-TST 2.2
9/13/2020
The quadratic equation
a
x
2
+
b
x
+
c
=
0
ax^2 + bx + c = 0
a
x
2
+
b
x
+
c
=
0
has its roots in the interval
[
0
,
1
]
[0, 1]
[
0
,
1
]
. Find the maximum of
(
a
−
b
)
(
2
a
−
b
)
a
(
a
−
b
+
c
)
\frac{(a - b)(2a - b)}{a(a - b + c)}
a
(
a
−
b
+
c
)
(
a
−
b
)
(
2
a
−
b
)
.
algebra
max
quadratic polynomial