MS112 Worksheet
Dr. Y. Kim
6.4 Quadratic Equations (Using 'Formula')
Quadratic Formula
Solve 0
2
=++ cbxax where
a
is nonzero
a
acbb
x
2
4
2
โยฑโ
=
The formula makes it easy to determine the nature of the roots without completely solving the
equation: Let
acbD 4
2
โ=
. Then
04
2
>โ= acbD
two real solutions
04
2
=โ= acbD
one real solution
04
2
<โ= acbD
two complex solutions
Ex1) Solve for x.
1.
015
2
=โ+ xx
2.
032
2
=โโ xx
3.
03
2
=โx
4.
2)23(
=
โ
xx
Ex2) Solve for x.
1.
1)1(4
โ
=
โ
xx
2.
0168
2
=+โ xx
Ex3) Solve for x.
1.
012
2
=++ xx
2.
013
2
=+โ xx
3.
0562
2
=โ+โ xx
6.5 More Quadratic Equations
Ex1) Solve for x.
1. 1
2
52 =
+
+
x
x
2.
3
52
1
4=+
+
x
x
Ex2) Solve for x.
1. 05421
24
=+โ xx 2. 045114
24
=โ+ xx
