1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard X
Mathematics
Relationship between Zeroes and Coefficients of a Polynomial
Find the valu...
Question
Find the values of p for which the quadratic equation
4
x
2
+
p
x
+
3
=
0
has equal roots.
If
α
a
n
d
β
a
r
e
t
h
e
z
e
r
o
s
o
f
t
h
e
p
o
l
y
n
o
m
i
a
l
6
y
2
-
7
y
+
2
,
f
i
n
d
a
q
u
a
d
r
a
t
i
c
p
o
l
y
n
o
m
i
a
l
w
h
o
s
e
z
e
r
o
s
a
r
e
1
α
a
n
d
1
β
.
Open in App
Solution
10
.
The
given
quadratic
equation
is
,
4
x
2
+
px
+
3
=
0
Now
,
a
=
4
;
b
=
p
;
c
=
3
Now
,
D
=
b
2
-
4
ac
=
p
2
-
48
For
equal
roots
,
D
=
0
⇒
p
2
-
48
=
0
⇒
p
2
=
48
⇒
p
=
±
4
3
11
.
Let
p
y
=
6
y
2
-
7
y
+
2
Now
,
α
+
β
=
-
coefficient
of
y
coefficient
of
y
2
=
7
6
Now
,
αβ
=
constant
term
coefficient
of
y
2
=
2
6
=
1
3
Now
,
1
α
and
1
β
are
the
zeroes
of
required
polynomial
.
Sum
of
zeroes
of
required
polynomial
,
S
=
1
α
+
1
β
=
α
+
β
αβ
=
7
/
6
1
/
3
=
7
6
×
3
1
=
7
2
Product
of
zeroes
of
required
polynomial
,
P
=
1
α
×
1
β
=
1
αβ
=
3
Now
,
required
polynomial
is
,
f
y
=
k
x
2
-
Sx
+
P
,
where
k
is
a
non
zero
real
number
=
k
x
2
-
7
x
2
+
3
=
k
2
2
x
2
-
7
x
+
6
=
2
x
2
-
7
x
+
6
On
taking
k
=
2
Suggest Corrections
1
Similar questions
Q.
If
α
and
β
are the zeroes of the polynomial
6
y
2
−
7
y
+
2
; find a quadratic polynomial whose zeroes are
1
α
+
1
β
.
Q.
If α and β are the zeros of the quadratic polynomial f(x) = x
2
− 2x + 3, find a polynomial whose roots are (i) α + 2, β + 2 (ii)
α
-
1
α
+
1
,
β
-
1
β
+
1
.
