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Discriminant Part 1
供稿人: Smith
(原作者: Tsygan)
The DISCRIMINANT is the part of the
Quadratic formula under the radical
The DISCRIMINANT tells you
 how many solutions (2, 1,or 0)
A Quadratic Equation, like x2 + 5x + 4, has.
The DISCRIMINANT is the part of the
Quadratic formula under the radical
Before working with the Quadratic Formula,
let's look at how radicals behave.
-9
9
0

=
=
ERROR
Before working with the Quadrartic Formula,
let's look at how radicals behave.
-9
9
0

=
=
ERROR
0
3
Example:     3 x 3   =               (not -9)
              
                (-3) x (-3) =            (not -9)

The square root of a negative number
is NOT a REAL number.

No real number times itself

will be negative.

Look at this example to see how ∓ shows up to 2 possible answers
The plus/minus shows two possible answers
10 ∓
10 ∓ √
9
The discriminant
equals b2 - 4ac
The plus/minus shows two possible answers
10 + 3 =
10 ∓
10 ∓ √
AND
3
9
The discriminant
equals b2 - 4ac
10 - 3 =
The plus/minus shows two possible answers
10 + 3 =
13
Solutions (roots) are 13 and 7.
10 ∓
10 ∓ √
AND
3
9
The discriminant
equals b2 - 4ac
10 - 3 =
A positive discriminant
(number under radical)
gives 2 solutions
7
The plus/minus shows two possible answers
40 ∓
40 ∓ √
0
The discriminant
equals b2 - 4ac
The plus/minus shows two possible answers
40 + 0 =
40 ∓
40 ∓ √
AND
0
0
The discriminant
equals b2 - 4ac
40 - 0 =
The plus/minus shows two possible answers
40 + 0 =
40
The solution (root) is 40
40 ∓
40 ∓ √
AND
0
0
The discriminant
equals b2 - 4ac
40 - 0 =
A zero discriminant
(number under radical)
gives 1 solution
40
7 + 4

 A positive discriminant,  such as 16,

 would give you _____  real solutions.

Example:
7 ∓ √16
7 - 4
  solution (s)
 zero

 two

 

 one

7 + 0

       A zero discriminant,  (0),

 would give you _____  real solutions.

Example:
7 ∓ √0
7 - 0
  solution (s)
 zero

 two

 

 one

7 + imaginary

       number

 A negative discriminant,  like -16,

 would give you _____  real solutions.

Example:
7 ∓ √-16

7 - imaginary

       number

  solution (s)
 zero

 two

 

 one

7 + √5

 A positive discriminant,  such as 5,

 would give you _____  real solutions.

Example:
7 ∓ √5
7 - √5
  solution (s)
 zero

 two

 

 one

Even though the √5 is not a perfect square,

it will still give you two real solutions.

 

The solutions will be irrational

(you can't get rid of the radical √      )

CLICK OK

Negative radicals like  √-7 and √-4

will give you         real solution(s)

Positive radicals like √9 and √5

will give you        real solution(s)

Zero radicals like √0

will give you          real solution(s)

2
?
0
?
1
?
Place
the 
correct
number
of 
solutions
under
each
quadratic
 1 Real
Solution
?
  2 RealSolutions
?
No RealSolution
?
ANSWERS
ANSWERS
ANSWERS
 1 RealSolution
  2 RealSolutions
No RealSolution

DISCRIMINANT

     PART  I

  COMPLETE

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