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Exercise:
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EXERCISE 2.1
EXERCISE 2.2
Q1
EXERCISE 2.1
The graphs of
y
=
p
(
x
)
y=p(x)
y
=
p
(
x
)
are given in Fig. 2.10 below, for some polynomials
p
(
x
)
p(x)
p
(
x
)
. Find the number of zeroes of
p
(
x
)
p(x)
p
(
x
)
, in each case.
Q1
EXERCISE 2.2
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
(i)
x
2
−
2
x
−
8
x^{2}-2 x-8
x
2
−
2
x
−
8
(ii)
4
s
2
−
4
s
+
1
4 s^{2}-4 s+1
4
s
2
−
4
s
+
1
(iii)
6
x
2
−
3
−
7
x
6 x^{2}-3-7 x
6
x
2
−
3
−
7
x
(iv)
4
u
2
+
8
u
4 u^{2}+8 u
4
u
2
+
8
u
(v)
t
2
−
15
t^{2}-15
t
2
−
15
(vi)
3
x
2
−
x
−
4
3 x^{2}-x-4
3
x
2
−
x
−
4
Q2
EXERCISE 2.2
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(i)
1
4
,
−
1
\frac{1}{4},-1
4
1
,
−
1
(ii)
2
,
1
3
\sqrt{2}, \frac{1}{3}
2
,
3
1
(iii)
0
,
5
0, \sqrt{5}
0
,
5
(iv)
1,1
(v)
−
1
4
,
1
4
-\frac{1}{4}, \frac{1}{4}
−
4
1
,
4
1
(vi)
4,1
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