AnswersCMS 2026-2027 NC Math 2 CREDIT RECOVERYComplex Numbers and Square Roots

Complex Numbers and Square Roots — Test Answers

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1
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What is the simplest form of square root of three comma zero two five ?

A
5 squared plus 11 squared
B
16
C
55
D
5 squared times 11 squared
2
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Which equation is equivalent to 5 cube root of x plus 8 is equal to 35 ?

A
cube root of x plus 8 is equal to 175
B
x plus 8 is equal to 21
C
x is equal to 351
D
x plus 8 is equal to 343
3

Which statement about the following equation is true? 3 x squared minus 8 x plus 5 is equal to 5 x squared

A
The discriminant is less than 0 , so there are two real roots.
B
The discriminant is greater than 0 , so there are two real roots.
C
The discriminant is less than 0 , so there are two complex roots.
D
The discriminant is greater than 0 , so there are two complex roots.
4

Which represents the reflection of f of x is equal to square root of x over the y -axis?

A
Image with description On a coordinate plane, an absolute value graph starts at (0, 0) and goes to the left through (negative 4, 2).
B
Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'f of x' Row 2: Column 1, 'negative 1'; Column 2, 'undefined' Row 3: Column 1, '0'; Column 2, '0' Row 4: Column 1, '1'; Column 2, '1' Row 5: Column 1, '4'; Column 2, '2'
C
Image with description On a coordinate plane, an absolute value graph starts at (0, 0) and goes up and to the left through (negative 2, 4).
D
Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'f of x' Row 2: Column 1, 'negative 1'; Column 2, '1' Row 3: Column 1, '0'; Column 2, '0' Row 4: Column 1, '1'; Column 2, 'negative 1' Row 5: Column 1, '4'; Column 2, 'negative 2'
5

What is the simplified form of square root of four hundred x to the hundredth power end root ?

A
two hundred x to the tenth power
B
twenty x to the fiftieth power
C
two hundred x to the fiftieth power
D
twenty x to the tenth power
6

In which quadrant is the number 6 minus 8 i located on the complex plane?

A
IV
B
III
C
II
D
I
7

Using the quadratic formula to solve 4 x squared minus 3 x plus 9 is equal to 2 x plus 1 , what are the values of x ?

A
the fraction with numerator 5 plus or minus square root of 103 i and denominator 8
B
the fraction with numerator 1 plus or minus square root of 159 i and denominator 8
C
the fraction with numerator 1 plus or minus square root of 153 and denominator 8
D
the fraction with numerator 5 plus or minus square root of 153 i and denominator 8
8

Which system is equivalent to the given system? 3 x squared minus 4 y squared is equal to 25 negative 6 x squared minus 2 y squared is equal to 11

A
6 x squared minus 8 y squared is equal to 50 negative 6 x squared minus 2 y squared is equal to 11
B
3 x squared minus 4 y squared is equal to 25 negative 12 x squared plus 4 y squared is equal to 22
C
6 x squared minus 8 y squared is equal to 25 negative 6 x squared minus 2 y squared is equal to 11
D
3 x squared minus 4 y squared is equal to 25 12 x squared plus 4 y squared is equal to 22
9

Which is the graph of g of x is equal to square root of x minus 16 end root ?

A
Image with description A coordinate plane with x-axis ranges from 4 to 44 in increments of 4 and y-axis ranges from 1 to 10 in increments of 1. A smooth curve originates from 16 comma 0, moves right and passes through the points 20 comma 2 and terminates at the point 40 comma 5.
B
Image with description A coordinate plane with x-axis ranges from 4 to 44 in increments of 4 and y-axis ranges from 1 to 10 in increments of 1. A smooth curve originates from 4 comma 0, moves right and passes through the point 20 comma 4 and terminates at the point 40 comma 6.
C
Image with description A coordinate plane with x-axis ranges from 4 to 44 in increments of 4 and y-axis ranges from 1 to 10 in increments of 1. A smooth curve originates from 4 comma 4, moves right and passes through the points 8 comma 6 and 28 comma 9.
D
Image with description A coordinate plane with x-axis ranges from 4 to 44 in increments of 4 and y-axis ranges from 1 to 10 in increments of 1. A smooth curve originates from 0 comma 4, moves right and passes through the points 4 comma 6 and 36 comma 10.
10

Solve for x in the equation x squared minus 12 x plus 36 is equal to 90

A
x is equal to 12 plus or minus 3 square root of 22
B
x is equal to 6 plus or minus 3 square root of 10
C
x is equal to 12 plus or minus 3 square root of 10
D
x is equal to 6 plus or minus 2 square root of 7
11

If x squared plus m x plus m is a perfect-square trinomial, which equation must be true?

A
x squared plus m x plus m is equal to open paren x plus 1 close paren squared
B
x squared plus m x plus m is equal to open paren x plus 2 close paren squared
C
x squared plus m x plus m is equal to open paren x plus 4 close paren squared
D
x squared plus m x plus m is equal to open paren x minus 1 close paren squared
12

Solve the radical equation x minus 7 is equal to square root of negative 4 x plus 28 end root Which statement is true about the solutions to the radical equation?

A
There is one extraneous solution, with a value greater than 4 .
B
There is one true solution, with a value greater than 6 .
C
There are no true solutions.
D
There are two true solutions.
13

Which statement about the following equation is true? 2 x squared minus 9 x plus 2 is equal to negative 1

A
The discriminant is greater than 0 , so there are two complex roots.
B
The discriminant is less than 0 , so there are two complex roots.
C
The discriminant is less than 0 , so there are two real roots.
D
The discriminant is greater than 0 , so there are two real roots.
14

The center of a circle is at the origin on a coordinate grid. A line with a positive slope intersects the circle at open paren 0 comma 7 close paren Which statement must be true?

A
The slope of the line is not equal to 7 .
B
The slope of the line is equal to 7 .
C
The circle has a radius equal to 7 .
D
The circle has a radius greater than 7 .
15

What is one of the solutions to the following system? y minus 3 is equal to x x squared minus 6 x plus 13 is equal to y

A
open paren 2 comma 5 close paren
B
open paren negative 5 comma 2 close paren
C
open paren negative 2 comma 1 close paren
D
open paren 8 comma 5 close paren
16

What is the value of the expression i to the 0 power times i to the 1th power times i squared times i cubed times i to the 4th power ?

A
1
B
negative i
C
negative 1
D
i
17

Solve for x in the equation x squared minus 8 x plus 41 is equal to 0

A
x is equal to 4 plus or minus 5 i
B
x is equal to negative 4 plus or minus square root of 37 i
C
x is equal to negative 4 plus or minus 5 i
D
x is equal to 4 plus or minus square root of 37 i
18

For what value of x is square root of the fraction with numerator 896 z to the 15th power and denominator 225 z to the 6th power end root is equal to the fraction with numerator x z to the 4th power and denominator 15 square root of 14 z ? Assume z is not equal to 0

A
8
B
4
C
64
D
16
19

What is the domain of the function?

A
all real numbers less than 0
B
all real number less than or equal to 0
C
all real numbers greater than or equal to 0
D
all real numbers
20

Which equation represents the graph of f of x ?

A
f of x is equal to square root of x plus 3
B
f of x is equal to square root of x minus 3
C
f of x is equal to square root of x plus 3
D
f of x is equal to square root of x minus 3

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