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Mathematics
Mathematics
Problem
Determine the quadratic polynomial
f
(
x
)
=
a
x
2
+
b
x
+
c
f(x)=ax^{2}+bx+c
f
(
x
)
=
a
x
2
+
b
x
+
c
that satisfies the following conditions: (i) The remainder obtained on division by
x
−
1
x-1
x
−
1
is
3
3
3
. (ii) The remainder obtained on division by
x
−
2
x-2
x
−
2
is
7
7
7
. (iii)
f
(
0
)
=
1
f(0)=1
f
(
0
)
=
1
.
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