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03.01.1
Chapter 03.01
Solution of Quadratic Equations
After reading this chapter, you should be able to:
1.
find the solutions of quadratic equations,
2.
derive the formula for the solution of quadratic equations,
3.
solve simple physical problems involving quadratic equations.
What are quadratic equations and how do we solve them?
A quadratic equation has the form
0
2
c
bx
ax
, where
0
a
The solution to the above quadratic equation is given by
a
ac
b
b
x
2
4
2
So the equation has two roots, and depending on the value of the discriminant,
ac
b
4
2
, the
equation may have real, complex or repeated roots.
If
0
4
2
ac
b
, the roots are complex.
If
0
4
2
ac
b
, the roots are real.
If
0
4
2
ac
b
, the roots are real and repeated.
Example 1
Derive the solution to
0
2
c
bx
ax
.
Solution
0
2
c
bx
ax
Dividing both sides by
a
,
0
a
, we get
0
2
a
c
x
a
b
x
Note if
0
a
, the solution to
0
2
c
bx
ax
is
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This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida  Tampa.
 Spring '08
 Kaw,A

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