Question 1

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. $3 z ^ { 2 } - 8 z - 3 = 0$

Accepted Answer

A) nonreal complex numbers, complex conjugates 
B) rational, unequal 
C) rational, equal 
D) irrational, unequal 
A) nonreal complex numbers, complex conjugates 
B) rational, unequal 
C) rational, equal 
D) irrational, unequal

Question 2

Simplify the expression. Enter the answer in a + bi form. $( 7 + \sqrt { - 15 } ) ( 3 - \sqrt { - 17 } )$

Accepted Answer

A)  $21 - \sqrt { 255 } + ( 3 \sqrt { 15 } + 7 \sqrt { 17 } ) i$ 
B)  $21 + \sqrt { 255 } + ( 3 \sqrt { 15 } + 7 \sqrt { 17 } ) i$ 
C)  $21 + \sqrt { 255 } + ( \sqrt [ 3 ] { 15 } - 7 \sqrt { 17 } ) i$ 
D)  $21 - \sqrt { 255 } + ( \sqrt [ 3 ] { 15 } - 7 \sqrt { 17 } ) i$ 
A)  $21 - \sqrt { 255 } + ( 3 \sqrt { 15 } + 7 \sqrt { 17 } ) i$ 
B)  $21 + \sqrt { 255 } + ( 3 \sqrt { 15 } + 7 \sqrt { 17 } ) i$ 
C)  $21 + \sqrt { 255 } + ( \sqrt [ 3 ] { 15 } - 7 \sqrt { 17 } ) i$ 
D)  $21 - \sqrt { 255 } + ( \sqrt [ 3 ] { 15 } - 7 \sqrt { 17 } ) i$

Question 3

Solve the inequality. $x ^ { 2 } - 8 x + 12 < 0$

Accepted Answer

A)  $x \in ( - 2,6 )$ 
B)  $x \in ( 4,8 )$ 
C)  $x \in ( - 8,4 )$ 
D)  $x \in ( 2,6 )$ 
E) no solution 
A)  $x \in ( - 2,6 )$ 
B)  $x \in ( 4,8 )$ 
C)  $x \in ( - 8,4 )$ 
D)  $x \in ( 2,6 )$ 
E) no solution

Question 4

Write $- 6 \sqrt { - 48 }$ in terms of i and simplify.

Accepted Answer

A)  $- 24 i \sqrt { 3 }$ 
B)  $24 i \sqrt { 3 i }$ 
C)  $- 24 \sqrt { 3 }$ 
D)  $- 6 i \sqrt { 3 }$ 
E)  $24 i \sqrt { 3 }$ 
A)  $- 24 i \sqrt { 3 }$ 
B)  $24 i \sqrt { 3 i }$ 
C)  $- 24 \sqrt { 3 }$ 
D)  $- 6 i \sqrt { 3 }$ 
E)  $24 i \sqrt { 3 }$

Question 5

Write the expression in $a + b i$ form. $\frac { \sqrt { 3 } + \sqrt { 2 } i } { \sqrt { 3 } - \sqrt { 2 } i }$

Accepted Answer

A)  $\frac { 6 } { 5 } + \frac { 2 } { 5 } i$ 
B)  $\frac { 1 } { 5 } - 2 \frac { \sqrt { 6 } } { 5 } i$ 
C)  $\frac { 5 } { 6 } + \frac { \sqrt { 6 } } { 5 } i$ 
D)  $\frac { 1 } { 5 } + 2 \frac { \sqrt { 6 } } { 5 } i$ 
E)  $\frac { 5 } { 6 } - \frac { \sqrt { 6 } } { 5 } i$ 
A)  $\frac { 6 } { 5 } + \frac { 2 } { 5 } i$ 
B)  $\frac { 1 } { 5 } - 2 \frac { \sqrt { 6 } } { 5 } i$ 
C)  $\frac { 5 } { 6 } + \frac { \sqrt { 6 } } { 5 } i$ 
D)  $\frac { 1 } { 5 } + 2 \frac { \sqrt { 6 } } { 5 } i$ 
E)  $\frac { 5 } { 6 } - \frac { \sqrt { 6 } } { 5 } i$

Question 6

Use the quadratic formula to find all real solutions of the equation. $x ^ { 2 } - 11 x + 24 = 0$

Accepted Answer

A) x = 6, x = 16 
B) x = 3, x = -8 
C) x = 3, x = 16 
D) x = -3, x = 8 
E) x = 3, x = 8 
A) x = 6, x = 16 
B) x = 3, x = -8 
C) x = 3, x = 16 
D) x = -3, x = 8 
E) x = 3, x = 8

Question 7

Simplify the expression. Enter the answer in a + bi form. $( 5 + 8 i ) + ( 1 - 3 i )$

Accepted Answer

A)  $6 - 5 i$ 
B)  $6 + 5 i$ 
C)  $29 + 7 i$ 
D)  $29 - 7 i$ 
A)  $6 - 5 i$ 
B)  $6 + 5 i$ 
C)  $29 + 7 i$ 
D)  $29 - 7 i$

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. $3 z ^ { 2 } - 8 z - 3 = 0$

Simplify the expression. Enter the answer in a + bi form. $( 7 + \sqrt { - 15 } ) ( 3 - \sqrt { - 17 } )$

Solve the inequality. $x ^ { 2 } - 8 x + 12 < 0$

Write $- 6 \sqrt { - 48 }$ in terms of i and simplify.

Write the expression in $a + b i$ form. $\frac { \sqrt { 3 } + \sqrt { 2 } i } { \sqrt { 3 } - \sqrt { 2 } i }$

Use the quadratic formula to find all real solutions of the equation. $x ^ { 2 } - 11 x + 24 = 0$

Simplify the expression. Enter the answer in a + bi form. $( 5 + 8 i ) + ( 1 - 3 i )$

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Polynomials

Rational Expressions

Exponents and Radicals

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Exponential and Logarithmic Functions

Filters

Exam 6: Quadratic Equations and Inequalities

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. 3z2−8z−3=03 z ^ { 2 } - 8 z - 3 = 03z2−8z−3=0

Simplify the expression. Enter the answer in a + bi form. (7+−15)(3−−17)( 7 + \sqrt { - 15 } ) ( 3 - \sqrt { - 17 } )(7+−15​)(3−−17​)

Solve the inequality. x2−8x+12<0x ^ { 2 } - 8 x + 12 < 0x2−8x+12<0

Write −6−48- 6 \sqrt { - 48 }−6−48​ in terms of i and simplify.

Write the expression in a+bia + b ia+bi form. 3+2i3−2i\frac { \sqrt { 3 } + \sqrt { 2 } i } { \sqrt { 3 } - \sqrt { 2 } i }3​−2​i3​+2​i​

Use the quadratic formula to find all real solutions of the equation. x2−11x+24=0x ^ { 2 } - 11 x + 24 = 0x2−11x+24=0

Simplify the expression. Enter the answer in a + bi form. (5+8i)+(1−3i)( 5 + 8 i ) + ( 1 - 3 i )(5+8i)+(1−3i)

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Polynomials

Rational Expressions

Exponents and Radicals

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Exponential and Logarithmic Functions

Filters

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. $3 z ^ { 2 } - 8 z - 3 = 0$

Simplify the expression. Enter the answer in a + bi form. $( 7 + \sqrt { - 15 } ) ( 3 - \sqrt { - 17 } )$

Solve the inequality. $x ^ { 2 } - 8 x + 12 < 0$

Write $- 6 \sqrt { - 48 }$ in terms of i and simplify.

Write the expression in $a + b i$ form. $\frac { \sqrt { 3 } + \sqrt { 2 } i } { \sqrt { 3 } - \sqrt { 2 } i }$

Use the quadratic formula to find all real solutions of the equation. $x ^ { 2 } - 11 x + 24 = 0$

Simplify the expression. Enter the answer in a + bi form. $( 5 + 8 i ) + ( 1 - 3 i )$