Quadratic Equations Worksheet With Answer Key Page 3
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1
2
3
4
5
6
72
or
(k + 2)
- 4.1.2k = 0
2
or
k
- 4k + 4 = 0
2
or
(k - 2)
= 0
hence k = 2.
B. Relation between roots and coefficients.
The general form of a quadratic equation is
2
ax
+ bx + c = 0
(i)
2
−
±
−
b
b
4
ac
On solving, x =
2
a
If α and β be two roots of the equation (i) such that
2
2
−
+
−
−
−
−
b
b
ac
b
b
ac
4
4
α=
and β=
a
a
2
2
then sum of the roots
= α + β
2
2
−
+
−
−
−
−
b
b
4
ac
b
b
4
ac
=
+
2
a
2
a
−
b
=
a
−
(
coefficien
t
of
x
)
=
2
coefficien
t
of
x
and the product of the roots
= α.β
2
2
−
+
−
−
−
−
b
b
4
ac
b
b
4
ac
=
×
2
a
2
a
c
=
a
consta
nt
term
=
2
coefficien
t
of
x
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