Additional Mathematics Module 3 - Quadratic Equations Worksheets With Answer Key Page 21
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332.2 FORMING A QUADRATIC EQUATIONS FROM GIVEN ROOTS and
Notes
If x
= a and x
= b
The quadratic equation with roots
1
2
and is written as
Then (x – a) = 0 and (x – b) = 0
(x – a)(x – b) = 0
2
)x + = 0 …….(1)
.x
– bx – ax + ab = 0
2
.x
– (
2
.x
– (a + b)x + ab = 0
Sum
Product
of the
.of the
Sum
Product
roots
of the
.of the
roots
roots
roots
2
From general form
ax
+ bx + c = 0
2
ax
bx
c
+
+
= 0
a
a
a
bx
c
2
.x
+
+
= 0 ……………………(2)
a
a
)x + = 0 ……….….(1)
2
Compare with the equations (1) and (2)
.x
– (
bx
c
2
x
+
+
= 0 ……………………(2)
a
a
b
– (
) =
c
b
(
) = -
( The sum of the roots)
c
c
=
( The product of the roots)
a
20
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