1. Among all pairs of numbers whose difference is 16, find a pair whose product is as small
as possible. What the numbers and what is the minimum product?
2. You have 600 feet of fencing to enclose a rectangular plot that borders on a river. If you
do not fence the side along the river, find the length and width of the plot that will
maximize the area. What is the largest area that can be enclosed?
Answers:
1. 8 and –8, –64
2. 150ft by 300ft, 45000 sqft

34
Unit 2-‐1 LT
12. I can use the discriminant to determine the number and type of solutions.
CP Algebra 2 Discriminant
Name ________________
Fill in the chart:
Equation
Standard
Form
Discriminant
Number and type of
Solutions/Roots
1.
6x
2
+ 3x + 4 = 0
2. x
2
= -6x - 9
3. 3x
2
– 6 = -5x
4. 2x
2
– x = -4

35
PRACTICE 5-8
Evaluate the discriminant of each equation. Tell how many solutions each equation has and whether the
solutions are real or imaginary.
1
y
=
x
2
+ 10
x
– 25
2.
y
=
x
2
+ 10
x
+ 10
3.
y
= 9
x
2
– 24
x
4.
y
= 4
x
2
– 4
x
+ 1
5.
y
= 4
x
2
– 5
x
+ 1
6.
y
= 4
x
2
– 3
x
+ 1
7.
y
=
x
2
+ 3
x
+ 4
8.
y
=
x
2
+ 7
x
– 3
9.
y
= –2
x
2
+ 3
x
– 5
10.
y
=
x
2
– 5
x
+ 4
11.
y
=
x
2
+ 12
x
+ 36
12.
y
=
x
2
+ 2
x
+ 3
13.
y
= 2
x
2
– 13
x
– 7
14.
y
= –5
x
2
+ 6
x
– 4
15.
y
= –4
x
2
– 4
x
– 1
ANSWERS:

36
Unit 2-1 LT 12 -
D55 Discriminant and Number of Solutions “Soil Erosion”

37
Unit 2-1 LT 12

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- Fall '19
- Quadratic equation, Elementary algebra