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Byju's Answer
Standard X
Mathematics
Formation of a Quadratic Equation From It's Roots
Solve this: ...
Question
Solve this:
Question NO.6 ) If {( – 1, 16), (0, 1), (1, 4) , (2, 25)}
⊂
f, where f : R
→
R, is a quadratic function, then the function f(x) is
(A) 9x
2
+ 6x +1
(B) 9x
2
– 6x + 1
(C) 3x
2
+ 2x + 1
(D) 3x
2
– 2x + 1
Open in App
Solution
-
1
,
16
,
0
,
1
,
1
,
4
,
2
,
25
⊂
f
f
:
ℝ
→
ℝ
f
c
o
n
t
a
i
n
s
e
l
e
m
e
n
t
s
-
1
,
16
,
0
,
1
,
1
,
4
a
n
d
2
,
25
f
-
1
=
16
f
0
=
1
f
1
=
4
a
n
d
s
o
o
n
.
.
.
S
i
n
c
e
f
x
i
s
q
u
a
d
r
a
t
i
c
L
e
t
f
x
=
a
x
2
+
b
x
+
c
f
0
=
1
0
+
0
+
c
=
1
c
=
1
f
x
=
a
x
2
+
b
x
+
1
f
1
=
4
a
+
b
+
1
=
4
a
+
b
=
3
_
_
_
_
_
_
_
_
1
f
-
1
=
16
a
-
b
+
1
=
16
a
-
b
=
15
_
_
_
_
_
_
_
_
_
_
_
2
A
d
d
i
n
g
e
q
u
a
t
i
o
n
1
a
n
d
2
2
a
=
18
a
=
9
a
-
b
=
15
9
-
b
=
15
b
=
-
6
f
x
=
9
x
2
-
6
x
+
1
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0
Similar questions
Q.
If
α
,
β
are the roots of
3
x
2
−
2
x
+
1
=
0
, then the equation whose roots are
−
α
3
,
−
β
3
is
Q.
Evaluate
3
x
2
−
x
−
4
9
x
2
−
16
÷
4
x
2
−
4
3
x
2
−
2
x
−
1
Q.
Simplify
3
x
2
−
x
−
4
9
x
2
−
16
÷
4
x
2
−
4
3
x
2
−
2
x
−
1
Q.
Assertion :Statement-1: Let
f
(
x
)
=
20
4
x
3
−
9
x
2
+
6
x
then the function
f
is unbounded. Reason: Statement-2 :
f
increases on
(
1
/
2
,
1
)
and decreases on
(
1
,
∞
)
∪
(
−
∞
,
1
/
2
)
.
Q.
Prove that the function
f
:
[
0
,
∞
)
→
R
given by
f
(
x
)
=
9
x
2
+
6
x
−
5
is not invertible. Modify the codomain of the function f to make it invertible, and hence find
f
−
1
.
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