Name:
Date:
Instructor:
Please use this template to insert your answers for the assignment. Please choose one of the three methods for showing your work (EE, ALT keys, or MathType). Remember that your work should be clear and legible. The ALT shortcut for radicals is ALT +251, √. Please note that it does not draw the full line above the sign. Therefore it will be assumed that anything that follows the √ is intended to be included under the radical. Using the superscript button above (in the font table), you can make powers; example: x2. You may also use Equation Editor as needed too.
Here is a formula that you will need. Feel free to copy/paste it as needed.
Quadratic formula:
INSTRUCTIONS: Read the references and examples found on the Background Info page. Work out the problems, showing all the computational steps. This is particularly important for those problems where the answer is given.
Problems 1 through 5: Find the roots (values of x when the expression is equal to zero) using factoring. Prove your answers are correct by checking, or showing that the values of x you computed satisfy the original equation.
1. Ans:
Calculations:
Check it:
Answer: _______________
2.
Calculations:
Check it:
Answer: _______________
3.
Calculations:
Check it:
Answer: _______________
4.
Calculations:
Check it:
Answer: _______________
5.
Calculations:
Check it:
Answer: _______________
Problems 6-10: Solve by completing the square. Prove your answers are correct by checking.
6. Ans:
Calculations:
Check it:
Answer: _______________
7.
Calculations:
Check it:
Answer: _______________
8.
Calculations:
Check it:
Answer: _______________
9.
Calculations:
Check it:
Answer: _______________
10.
Calculations:
Check it:
Answer: _______________
Problems 11 to 15: Solve by using the quadratic formula. Prove your answers are correct by checking.
11. Ans:
Calculations:
Check it:
Answer: _______________
12.
Calculations:
Check it:
Answer: _______________
13.
Calculations:
Check it:
Answer: _______________
14.
Calculations:
Check it:
Answer: _______________
15.
Calculations:
Check it:
Answer: _______________
Problems 16, 17: Determine the number and type of root(s) for each equation. Use the discriminant, (b2-4ac).
16.
Calculations:
Answer: _______________
17.
Calculations:
Answer: _______________
Problems 18 through 20: Consider the quadratic equation
18. For what value of c does the equation have one real root? (Hint: Using the values of a and b found in the equation, solve D = 0 for c.)
Calculations:
Answer: _______________
19. For what range of values does the equation have two real roots? (Hint: The answer is an inequality. Don't simply offer examples of c that satisfy the requirement.)
Calculations:
Answer: _______________
20. For what range of values does the equation have two complex roots?
Calculations:
Answer: _______________
2
x14x450
++=
16
x8
x
+=
2
3x21x0
+=
2
x4x30
++=
x1,3
=--
2
x5x10
+-=
2
2x7x150
+-=
2
1
x7x16
2
-=
x(x5)4
-=-
2
x90
-=
x3
=±
2
x90
+=
2
x3x40
-+=
2
2x3x60
++=
(
)
2
5x1130
++=
x(x3)2
+=
2x(x2)2
+=-
2
x4xc0.
++=
2
4x250
-=
5
x
2
=±
2
x12x360
-+=
gasimm
mat101_case_4_answer_template.docx
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