Q.
Find the zeroes of the following quadratics Polynomials.
(1)
Sol.
m2 – 84
m2 – 84
m2
84
–
a2 – b2
(a + b)
(a – b)
=
(m)2
–
=
=
(m
+
(m
+
(m
–
(m
–
∴
So, the value of m2 – 84 is zero
When
=
0
or
=
0
(m
(m
(m
(m
∴
m
+
=
0
or
m
–
=
0
∴
or
m
=
m
=
84
42
21
2
2
3
7
7
1
–
∴
∴
or
m
=
m
=
–
Q.
Find the zeroes of the following quadratics Polynomials.
(2)
Sol.
x2 + 21x – 196
x2
+
21x
–
196
x2 + 21x – 196
=
x2
–
196
+
196
28
7
–
x
x
=
x
(28x
–
7x)
=
x2
+
28x
–
7x
–
196
=
x
(x
+
28)
–
7
(x
+
28)
=
(x
+
28)
(x
–
7)
(x + 28)
21
21
∴
x
+
28
=
0
or
x
–
7
=
0
∴
x
=
–28
or
x
=
7
∴
The zeroes of x2 + 21x – 196 are –28 and 7.
∴
(x + 28) and (x – 7) are the factors of
x2 + 21x – 196
So, the value of x2 + 21x – 196 is zero
When
(x + 28)
=
0
or
(x – 7)
=
0