Question

solve the following quadratic equation p squared + x squared (p squared - q squared) x -q squared = 0

Answer 1

We can Split the Middle Term of this expression to factorise it

In this technique, if we have to factorise an expression like
a
x
2
+
b
x
+
c
, we need to think of 2 numbers such that:

N
1
⋅
N
2
=
a
⋅
c
=
1
⋅
24
=
24

AND
N
1
+
N
2
=
b
=
−
10

After trying out a few numbers we get
N
1
=
−
6
and
N
2
=
−
4

−
6
⋅
−
4
=
24
, and
(
−
6
)
+
(
−
4
)
=
−
10

x
2
−
10
x
+
24
=
x
2
−
6
x
−
4
x
+
24

=
x
(
x
−
6
)
−
4
(
x
−
6
)

(
x
−
6
)
is a common factor to each of the terms

=
(
x
−
6
)
(
x
−
4
)