(Q5) Show that the sum of the roots of a quadratic equation ax
2
+ bx + c = 0 is
-b
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
Sum of the roots
=
-b + √(b
2
-
c)
2
+ (
-b-√(b
2
-
c)
2
)
=
-b + √(b
2
-
c) - b - √(b
2
-
c)
2
=
-2b
2a
=
-b
a
∴sum of roots of a quadratic equation is
-b
a
Clear