Question 1

Factor the trinomial square and use the square root method to solve the equation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

D

Question 2

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. 
A) nonreal complex numbers, complex conjugates
B) rational, unequal
C) irrational, unequal
D) rational, equal
E) irrational, equal

Accepted Answer

The discriminant, b^2-4ac, determines the nature of the solutions of the quadratic equation. If it is positive, the solutions are irrational and unequal; if it is zero, the solutions are rational and equal; if it is negative, the solutions are nonreal complex numbers, meaning they cannot be expressed as a real number. Since the discriminant is not given and we are only asked to determine the type of solutions that exist, we can use process of elimination. Option A can be eliminated because it refers to nonreal complex numbers, which are only possible if the discriminant is negative. Option B can be eliminated because it refers to rational and unequal solutions, which are only possible if the discriminant is positive but not a perfect square. Option D can be eliminated because it refers to rational and equal solutions, which are only possible if the discriminant is a perfect square. Therefore, the best choice is C, irrational and unequal solutions, which are possible for any non-zero value of the discriminant.

Question 3

Factor the trinomial square and use the square root method to solve the equation. 
A)  , 
B)  , 
C)  , 
D)  ,

Accepted Answer

C

Question 4

Use the method of completing the square to solve the quadratic equation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use the method of completing the square...

Question 5

Use the method of completing the square to solve the quadratic equation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The quadratic equation is in the form $ax^2+bx+c=0$. To complete the square, we need to make sure that the coefficient of $x^2$ is 1. We can do this by dividing both sides of the equation by 11.
$$x^2-\frac{16}{11}x=-\frac{40}{11}$$
Next, we need to add and subtract $(\frac{16}{11})^2/4$ to the left-hand side of the equation:
$$x^2-\frac{16}{11}x+(\frac{16}{11})^2/4-(\frac{16}{11})^2/4=-\frac{40}{11}$$
Simplifying the left-hand side:
$$(x-\frac{8}{11})^2-\frac{64}{121}=-\frac{40}{11}$$
Adding $\frac{64}{121}$ to both sides of the equation:
$$(x-\frac{8}{11})^2=\frac{144}{121}$$
Taking the square root of both sides:
$$x-\frac{8}{11}=\pm\frac{12}{11}$$
Solving for x:
$$x=\frac{20}{11}, \frac{-4}{11}$$
Therefore, the answer is choice B.

Question 6

When a wholesaler sells  CD players, the revenue is  . How many CD players would the wholesaler have to sell to receive  ?
A)  CD players
B)  CD players
C)  CD players
D)  CD players
E)  CD players

Accepted Answer

The answer of When a wholesaler sells  CD players,...

Question 7

Use the factoring method to solve the equation. 
A)  , 
B)  , 
C)  , 
D)  , 
E)  ,

Accepted Answer

The answer of Use the factoring method to solve the...

Question 8

Solve the equation by completing the square. 
A)  , 
B)  , 
C)  , 
D)  , 
E)  ,

Accepted Answer

The answer of Solve the equation by completing the square....

Question 9

The distance (in feet) that an object will fall in  seconds is given by the formula  . How long will it take an object to fall 784 feet?
A) 7 sec
B) 49 sec
C) 9 sec
D) 6 sec
E) 48 sec

Accepted Answer

The answer of The distance (in feet) that an object...

Question 10

Use the square root method to solve the equation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use the square root method to solve...

Question 11

Use the quadratic formula to find all real solutions of the equation. 
A) x = 10, x = 4
B) x = 5, x = -2
C) x = 5, x = 4
D) x = -5, x = 2
E) x = 5, x = 2

Accepted Answer

Since the quadratic formula is used to find solutions for quadratic equations in the form ax^2+bx+c=0, we need to first put the given equation into this form:

x^2 - 7x - 10 = 0

Using the quadratic formula: 
x = (-b ± sqrt(b^2 - 4ac)) / 2a

We plug in a = 1, b = -7, and c = -10, then simplify:

x = (7 ± sqrt(49 + 40)) / 2
x = (7 ± sqrt(89)) / 2

These solutions are both real numbers, and they match the options E) x = 5, x = 2.

Question 12

The height in feet  of a rocket in flight is given by the formula  , where  is the time of the flight in seconds. How long will it take for the rocket to hit the ground?
A) 11 sec
B) 10 sec
C) 8 sec
D) 12 sec
E) 13 sec

Accepted Answer

The answer of The height in feet  of a...

Question 13

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. 
A) nonreal complex numbers, complex conjugates
B) rational, unequal
C) rational, equal
D) irrational, unequal

Accepted Answer

The answer of Use the discriminant to determine what type...

Question 14

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. 
A) rational, equal
B) irrational, unequal
C) irrational, equal
D) nonreal complex numbers, complex conjugates
E) rational, unequal

Accepted Answer

The discriminant is the expression under the square root in the quadratic formula, which is b^2-4ac. If the discriminant is negative, the solutions will be nonreal complex numbers, which will be complex conjugates since the coefficients of the quadratic equation are real. Therefore, the answer is D.

Question 15

What is the first step to solving x ² 10 x = 56 by completing the square? A) Add 25 to both sides. B) Add -25 to both sides C) Subtract 56 from both sides. D) Isolate x ². E) none of these

Accepted Answer

The answer of What is the first step to solving...

Question 16

Complete the square and factor the resulting perfect-square trinomial. 
A) ( t + 16 ) 
B) ( t - 4 ) 
C) ( t + 4 ) 
D) ( t - 16 )

Accepted Answer

To complete the square, we need to take half of the coefficient of the t-term, square it, and add it to both sides. 
$$t^2 + 8t + 16 = (t + 4)^2$$
The resulting perfect-square trinomial is $(t + 4)^2$, which corresponds to choice C.

Question 17

Use the quadratic formula to find all real solutions of the equation. 
A) 
B) 
C) 
D) 
E) no real solutions

Accepted Answer

The answer of Use the quadratic formula to find all...

Question 18

Complete the square and factor the resulting perfect-square trinomial. 
A) ( 8 t +  ) 
B) ( 8 t -  ) 
C) ( 8 t +  ) 
D) ( 8 t -  )

Accepted Answer

We can complete the square as follows:
$8t^2+11t-15 = 8\left(t+\frac{11}{16}\right)^2 - \frac{121}{32} - 15$
$= 8\left(t+\frac{11}{16}\right)^2 - \frac{481}{32}$
So we have a perfect-square trinomial with $a=8$, $b=\frac{11}{16}$, and $c=-\frac{481}{32}$. To factor this, we can use the form $(a+b)^2 = a^2 + 2ab + b^2$ with $a=2\sqrt{2}t$ and $b=\frac{11\sqrt{2}}{8}$:
$8\left(t+\frac{11}{16}\right)^2 - \frac{481}{32} = 8\left(\left(\sqrt{2}t\right)^2 + 2\left(\sqrt{2}t\right)\left(\frac{11\sqrt{2}}{8}\right) + \left(\frac{11\sqrt{2}}{8}\right)^2\right) - \frac{481}{32}$
$= 8\left(2t+\frac{11\sqrt{2}}{4}\right)^2 - \frac{481}{32}$
So the correct choice is (C).

Question 19

The area of a circle is numerically equal to 8 times the circumference of the circle. Find the length of a radius of the circle.
A) 16 
B) 17
C) 16
D) 15 
E) 8

Accepted Answer

Let r be the radius of the circle. The area of the circle is equal to πr^2, and the circumference of the circle is equal to 2πr. We know that:

πr^2 = 8(2πr)

Dividing both sides by πr, we get:

r = 16

Therefore, the length of the radius is 16, and the correct answer is choice C.

Question 20

Solve the equation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Solve the equation. 
A) 
B) 
C) 
D)...

Quiz 9: Quadratic Equations, Quadratic Functions, and Complex Numbers

Factor the trinomial square and use the square root method to solve the equation.

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation.

Factor the trinomial square and use the square root method to solve the equation.

Use the method of completing the square to solve the quadratic equation.

Use the method of completing the square to solve the quadratic equation.

When a wholesaler sells CD players, the revenue is . How many CD players would the wholesaler have to sell to receive ?

Use the factoring method to solve the equation.

Solve the equation by completing the square.

The distance (in feet) that an object will fall in seconds is given by the formula . How long will it take an object to fall 784 feet?

Use the square root method to solve the equation.

Use the quadratic formula to find all real solutions of the equation.

The height in feet of a rocket in flight is given by the formula , where is the time of the flight in seconds. How long will it take for the rocket to hit the ground?

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation.

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation.

What is the first step to solving x 2 10 x = 56 by completing the square?

Complete the square and factor the resulting perfect-square trinomial.

Use the quadratic formula to find all real solutions of the equation.

Complete the square and factor the resulting perfect-square trinomial.

The area of a circle is numerically equal to 8 times the circumference of the circle. Find the length of a radius of the circle.

Solve the equation.

What is the first step to solving x ² 10 x = 56 by completing the square?