Sol.
f(t)
Q.
If and β are the zeros of the quadratic polynomial f(t) = t2 – 4t + 3, find the value of 4β3 + 3β4.
=
t2
–
4t
+
3
Here
a
=
1,
b
=
–4,
c
=
3
and β are the zeros of f(t)
∴
+
β
=
a
–b
=
=
4
β
=
a
c
=
1
3
1
–
4β3
=
(β)3
( + β)
=
=
27
×
4
=
108
and
=
3
+
3β4
=
3β3
(
(3)3
×
4
1
+
β
)
(–4)
4β3
+
3β4
=
∴
108
Sol.
p(s)
Q.
=
3s2
–
6s
+
4
Here
a
=
3,
b
=
–6,
c
=
4
and β are the zeros of p(s)
∴
+
β
=
a
–b
=
If and β are the zeros of the quadratic polynomial p(s) = 3s2 – 6s + 4,
find the value of
+
β
β
+ 2
+ 3β.
+
1
β
1
+
1
β
1
=
2
3
(–6)
–
and
β
=
a
c
=
3
4
β
+
β
+
2
+
3β
=
β
2
+
β2
+
2
β
+
β
+
3β
=
β
( + β)2
–
2β
+
2
β
+
β
+
3β
🗹
+
β
2
β
6
Sol.
=
(2)2
–
3
2
4
3
4
+
2
4
2
3
+
3
4
3
÷
=
4
–
3
8
3
4
+
2
3
2
4
×
+
4
2
=
12
–
3
8
÷
3
4
+
3
+
4
=
3
4
×
4
3
+
7
=
1
+
7
=
8
p(s)
=
3s2
–
6s
+
4
+
β
=
2
=
β
( + β)2
–
2β
+
2
+
β
β
+
3β
+
1
β
1
β
+
β
+
2
+
3β
∴
=
8
Q.
β
=
a
c
=
3
4
and
1
1
1
If and β are the zeros of the quadratic polynomial p(s) = 3s2 – 6s + 4,
find the value of
+
β
β
+ 2
+ 3β.
+
1
β
1