Algebra Solving Quadratic Equations Question

Kuta Software – Infinite Algebra 1Name___________________________________
Solving Quadratic Equations by Factoring
Date________________ Period____
Solve each equation by factoring.
1) (k + 1)(k − 5) = 0
2) (a + 1)(a + 2) = 0
3) (4k + 5)(k + 1) = 0
4) (2m + 3)(4m + 3) = 0
5) x 2 − 11 x + 19 = −5
6) n 2 + 7n + 15 = 5
7) n 2 − 10n + 22 = −2
8) n 2 + 3n − 12 = 6
9) 6n 2 − 18n − 18 = 6
10) 7r 2 − 14r = −7
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Worksheet by Kuta Software LLC
11) n 2 + 8n = −15
12) 5r 2 − 44r + 120 = −30 + 11r
13) −4k 2 − 8k − 3 = −3 − 5k 2
14) b 2 + 5b − 35 = 3b
15) 3r 2 − 16r − 7 = 5
16) 6b 2 − 13b + 3 = −3
17) 7k 2 − 6k + 3 = 3
18) 35k 2 − 22k + 7 = 4
19) 7 x 2 + 2 x = 0
20) 10b 2 = 27b − 18
21) 8 x 2 + 21 = −59 x
22) 15a 2 − 3a = 3 − 7a
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Worksheet by Kuta Software LLC
Kuta Software – Infinite Algebra 1
Name___________________________________
Solving Quadratic Equations by Factoring
Date________________ Period____
Solve each equation by factoring.
1) (k + 1)(k − 5) = 0
2) (a + 1)(a + 2) = 0
{−1, 5}
{−1, −2}
3) (4k + 5)(k + 1) = 0
{
5
− , −1
4
4) (2m + 3)(4m + 3) = 0
}
5) x 2 − 11 x + 19 = −5
{
3 3
− ,−
2 4
6) n 2 + 7n + 15 = 5
{3, 8}
7) n 2 − 10n + 22 = −2
{−5, −2}
8) n 2 + 3n − 12 = 6
{6, 4}
9) 6n 2 − 18n − 18 = 6
{3, −6}
10) 7r 2 − 14r = −7
{1 }
{4, −1}
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}
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Worksheet by Kuta Software LLC
11) n 2 + 8n = −15
12) 5r 2 − 44r + 120 = −30 + 11r
{−5, −3}
{6, 5}
13) −4k 2 − 8k − 3 = −3 − 5k 2
14) b 2 + 5b − 35 = 3b
{8, 0}
{−7, 5}
15) 3r 2 − 16r − 7 = 5
16) 6b 2 − 13b + 3 = −3
{ }
{ }
2
− ,6
3
2 3
,
3 2
17) 7k 2 − 6k + 3 = 3
18) 35k 2 − 22k + 7 = 4
{ }
{ }
6
,0
7
1 3
,
5 7
19) 7 x 2 + 2 x = 0
20) 10b 2 = 27b − 18
{ }
{ }
2
− ,0
7
6 3
,
5 2
21) 8 x 2 + 21 = −59 x
{
3
− , −7
8
22) 15a 2 − 3a = 3 − 7a
{ }
1 3
,−
3 5
}
Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com
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Worksheet by Kuta Software LLC
Kuta Software – Infinite Algebra 1
Name___________________________________
Using the Quadratic Formula
Date________________ Period____
Solve each equation with the quadratic formula.
1) m 2 − 5m − 14 = 0
2) b 2 − 4b + 4 = 0
3) 2m 2 + 2m − 12 = 0
4) 2 x 2 − 3 x − 5 = 0
5) x 2 + 4 x + 3 = 0
6) 2 x 2 + 3 x − 20 = 0
7) 4b 2 + 8b + 7 = 4
8) 2m 2 − 7m − 13 = −10
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Worksheet by Kuta Software LLC
9) 2 x 2 − 3 x − 15 = 5
10) x 2 + 2 x − 1 = 2
11) 2k 2 + 9k = −7
12) 5r 2 = 80
13) 2 x 2 − 36 = x
14) 5 x 2 + 9 x = −4
15) k 2 − 31 − 2k = −6 − 3k 2 − 2k
16) 9n 2 = 4 + 7n
17) 8n 2 + 4n − 16 = −n 2
18) 8n 2 + 7n − 15 = −7
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Worksheet by Kuta Software LLC
Kuta Software – Infinite Algebra 1
Name___________________________________
Using the Quadratic Formula
Date________________ Period____
Solve each equation with the quadratic formula.
1) m 2 − 5m − 14 = 0
2) b 2 − 4b + 4 = 0
{2 }
{7, −2}
3) 2m 2 + 2m − 12 = 0
4) 2 x 2 − 3 x − 5 = 0
{2, −3}
{ }
5
, −1
2
5) x 2 + 4 x + 3 = 0
6) 2 x 2 + 3 x − 20 = 0
{−1, −3}
{ }
5
, −4
2
7) 4b 2 + 8b + 7 = 4
{
1 3
− ,−
2 2
8) 2m 2 − 7m − 13 = −10
{
}
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-1-
7+
4
73 7 −
,
73
4
}
Worksheet by Kuta Software LLC
9) 2 x 2 − 3 x − 15 = 5
10) x 2 + 2 x − 1 = 2
{1, −3}
{ }
4, −
5
2
11) 2k 2 + 9k = −7
{
−1, −
7
2
12) 5r 2 = 80
{4, −4}
}
13) 2 x 2 − 36 = x
14) 5 x 2 + 9 x = −4
{ }
{
4
− , −1
5
9
, −4
2
15) k 2 − 31 − 2k = −6 − 3k 2 − 2k
16) 9n 2 = 4 + 7n
{
{ }
5 5
,−
2 2
17) 8n 2 + 4n − 16 = −n 2
{
−2 + 2 37 −2 − 2 37
,
9
9
}
7+
193 7 − 193
,
18
18
}
18) 8n 2 + 7n − 15 = −7
}
{
−7 + 305 −7 − 305
,
16
16
}
Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com
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CORNELL NOTES
SHEET
QUESTIONS
Name:
Class: MAC1105 Topic: ______Quadratic Notes __________________
Date: 02_____/ __28___/ ____2022____
Period Spring Semester ______
NOTES
SUMMARY: Write 4 or more sentences describing specific learning from these notes.
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
CORNELL NOTES
SHEET
QUESTIONS
Name: ________John Doe_________________________
Class: ___MAC1105___________ Topic: _Complex Numbers___
Date: ____01___/ _04___/ __2022____
Period _Spring 2022___
NOTES
The imaginary unit is denoted by the letter “i”, and i = sqrt (-1)
Addition: (3 + 3i) + (2 – i) = 3 + 3i + 2 – i = 5 – 2i
Subtraction: (4 + 3i) – (-2 – 5i) = 4 + 3i + 2 + 5i = 6 + 8i
Why were called imaginary?
Multiplication: 4( 3 + 2i) = 4(3) + 4(2i) = 12 + 8i
Who introduced the complex
numbers in Math?
Complex conjugate of a + bi is a – bi
Division: 3/(2 + i) = 3(2 -i)/(2+i)(2-i) = (6 – 3i)/ (4 +1) = (6 – 3i)/5 =
= 6/5 – 3i/5
How are complex numbers
used in real life?
Powers of i: i^ 21. Divide 21 by 4, the remainder 1 is the new exponent, so
I^21 = i^1 = i
SUMMARY: Write 4 or more sentences describing specific learning from these notes.
__________________________________________________________________________________________
__I learned what a complex number is; the different operations that we can perform: addition, subtraction, _
__multiplication, division, and powers of i. _______________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
Test Content
Question 1
Solve the equation by factoring.
12×2 + 23x + 10 = 0
Question 2
Solve the equation by factoring.
7 – 7x = (4x + 9)(x – 1)
{-4, 1}
{-1, 4}
Question 3
Solve the equation by factoring.
4×2 – 7x = 2
{-4, 2}
Question 4
Solve the equation by factoring.
2×2 – 15x = 8
{-2, 8}
Question 5
Solve the equation by factoring.
2x(x – 5) = 6×2 – 11x
{0}
{0, 4}
Question 6
Perform the indicated operations and write the result in standard form.
Question 7
Perform the indicated operations and write the result in standard form.
-6
6
6i2
-6i
Question 8
Perform the indicated operations and write the result in standard form.
32i
-12i
-12
12i
Question 9
Perform the indicated operations and write the result in standard form.
Question 10
Perform the indicated operations and write the result in standard form.
Question 11
Complex numbers are used in electronics to describe the current in an electric circuit. Ohm’s law relates
the current in a circuit, I, in amperes, the voltage of the circuit, E, in volts, and the resistance of the
circuit, R, in ohms, by the formula Solve the problem using this formula.
Find E, the voltage of a circuit, if I = (2 + 5i) amperes and R = (8 + 2i) ohms.
(44 – 6i) volts
(6 – 44i) volts
(44 + 6i) volts
(6 + 44i) volts
Question 12
Complex numbers are used in electronics to describe the current in an electric circuit. Ohm’s law relates
the current in a circuit, I, in amperes, the voltage of the circuit, E, in volts, and the resistance of the
circuit, R, in ohms, by the formula Solve the problem using this formula.
Find E, the voltage of a circuit, if I = (16 + i) amperes and R = (2 + 4i) ohms.
(28 + 66i) volts
(-32 – 66i) volts
(-32 + 66i) volts
(28 – 66i) volts
Question 13
Perform the indicated operations and write the result in standard form.
(3 + i)2 – (2 – i)2
-5 + 10i
5 – 10i
5 + 10i
-5
Question 14
Perform the indicated operations and write the result in standard form.
(3 + i)2 – (2 – i)2
5 + 10i
-5
-5 + 10i
5 – 10i
Question 15
Find the product and write the result in standard form.
(7 + 3i)(7 – 3i)
49 – 9i2
58
40
49 – 9i
Question 16
Compute the discriminant. Then determine the number and type of solutions for the given equation.
6×2 = -8x – 7
232; two unequal real solutions
0; one real solution
-104; two complex imaginary solutions
Question 17
Compute the discriminant. Then determine the number and type of solutions for the given equation.
x2 + 4x + 3 = 0
4; two unequal real solutions
0; one real solution
-28; two complex imaginary solutions
Question 18
Compute the discriminant. Then determine the number and type of solutions for the given equation.
x2 + 7x + 6 = 0
-73; two complex imaginary solutions
0; one real solution
25; two unequal real solutions
Question 19
Solve the equation by completing the square.
x2 – 12x – 11 = 0
Question 20
Determine the constant that should be added to the binomial so that it becomes a perfect square
trinomial. Then write and factor the trinomial.
x2 – 8x
64; x2 – 8x + 64 = (x – 8) 2
-64; x2 – 8x – 64 = (x – 8) 2
16; x2 – 8x + 16 = (x – 4) 2
-16; x2 – 8x – 16 = (x – 4) 2
Question 21
Determine the constant that should be added to the binomial so that it becomes a perfect square
trinomial. Then write and factor the trinomial.
x2 – 18x
324; x2 – 18x + 324 = (x – 18) 2
-81; x2 – 18x – 81 = (x – 9) 2
81; x2 – 18x + 81 = (x – 9) 2
-324; x2 – 18x – 324 = (x – 18) 2
Question 22
Solve the equation by completing the square.
x2 – 6x + 34 = 0
{3 ± 25i}
{3 + 5i}
{8, -2}
{3 ± 5i}
Question 23
Determine the constant that should be added to the binomial so that it becomes a perfect square
trinomial. Then write and factor the trinomial.
x2 – 13x
Question 24
Solve the equation by completing the square.
16×2 – 5x + 1 = 0
Question 25
Solve the equation by completing the square.
x2 + 4x – 9 = 0
Question 26
Divide and express the result in standard form.
-i
– +i
-i
– -i
Question 27
Divide and express the result in standard form.
+i
-i
-i
+i
Question 28
Divide and express the result in standard form.
1 + 2i
1 + 5i
1 – 2i
-1 + 2i
Question 29
Divide and express the result in standard form.
-i
-i
-i
-i
Question 30
Divide and express the result in standard form.
-1
i
-i
1
Question 31
Solve the equation using the quadratic formula.
3×2 + 10x + 6 = 0
Question 32
Solve the equation using the quadratic formula.
9×2 + 7x + 3 = 0
Question 33
Solve the equation using the quadratic formula.
5×2 + x – 2 = 0
Question 34
Solve the equation using the quadratic formula.
4×2 + 5x + 7 = 0
Question 35
Solve the equation using the quadratic formula.
x2 + 14x + 85 = 0
{-1, -13}
{-7 + 6i}
{-7 + 6i, -7 – 6i}
{-7 – 36i, -7 + 36i}
Question 36
Add or subtract as indicated and write the result in standard form.
(6 – 2i) + (8 + 7i)
14 + 5i
-14 – 5i
-2 + 9i
14 – 5i
Question 37
Add or subtract as indicated and write the result in standard form.
(6 – 10i) + (7 + 7i) + (-4 – 5i)
13 – 3i
-5 – 22i
17 + 2i
9 – 8i
Question 38
Add or subtract as indicated and write the result in standard form.
(-5 + 3i) – 9
14 – 3i
4 – 3i
-14 + 3i
4 + 3i
Question 39
Add or subtract as indicated and write the result in standard form.
(3 – 4i) + (4 + 9i)
7 + 5i
7 – 5i
-7 – 5i
-1 + 13i
Question 40
Add or subtract as indicated and write the result in standard form.
4i – (-8 – i)
-8 + 3i
8 – 3i
8 + 5i
-8 – 5