The

1
Chapter 4 Quadratic and Polynomial Equations
4.5
The Quadratic Formula
4.5.1
MATHPOWERTM 11, WESTERN EDITION
2
The Quadratic Formula
The solution of the quadratic equation ax2 bx
c 0 can be found by using the quadratic
formula
4.5.2
3
Solving Quadratic Equations Using the Quadratic
Formula
a 2, b -5, c 2
Solve 2x2 - 5x 2 0.
or
x 2
4.5.3
4
Solving Quadratic Equations Using the Quadratic
Formula
Solve x2 - 6x 7 0.
4.5.4
5
Solving Quadratic Equations With No Real Roots
Solve x2 - 5x 7 0.
Since
is not defined by real numbers, then this
equation has NO REAL ROOTS.
4.5.5
6
Solving Quadratic Equations With No Real Roots -
Using Complex Numbers
An equation such as x2 1 0 (x2 -1) has no
solution in the set of real numbers. But, by
extending the number system, we can give meaning
to the solution of this equation. We do this by
defining i with the property that
i2 -1 or i v - 1
Since there is no real number that has its square
as a negative, the number i is not a real
number. It cannot be expressed as a decimal and
it can not be expressed as a point on the number
line. For these reasons, the square roots of
negative numbers are called imaginary numbers.
4.5.6
7
Solving Quadratic Equations With No Real Roots
Solve x2 - 6x 13 0.
4i
The roots of the equation are x 3 2i and x
3 - 2i.
4.5.7
8
Assignment
Suggested Questions
Page 178 7, 13, 16, 21, 26, 33, 34, 47
Pages 185 and 186 1-15 odd 64, 72, 76
4.5.8