(Q6)Show that the product of the roots of a quadratic equation ax
2
+ bx + c = 0 is
c
a
Answer:
Let the quadratic equation = ax
2
+ bx + c = 0(a≠0)
ax
2
+ bx = -c
x
2
+
b
a
x =
-c
x
2
+2
b
a
x(
1
2
) =
-c
x
2
+ 2.x(
b
2a
) =
-c
x
2
+ 2.x.
b
2a
+ (
b
2a
)
2
=
-c
+ (
b
)
2
(x +
b
2a
)
2
=
b
2
2
-
c
=
b
2
-
c
4
2
x +
b
2a
=
√(b
2
-
c)
2
x = -
b
2a
±
√(b
2
-
c)
2
=
-b + √(b
2
-
c)
2
,
-b - √(b
2
-
c)
2
Product of the roots
= [
-b + √(b
2
-
c)
2
] × [
-b - √(b
2
-
c)
2
]
=[
-b
2a
]
2
- [
√(b
2
-
c)
2
]
=
b
2
4a
2
-
(b
2
-4ac)
4a
2
=
b
2
-b
2
+4ac
4a
2
=
4ac
4a
2
=
c
a
Clear