Question 1

Which one refers to a polynomial equation in the form

ax^2 + bx + c = 0

where a, b, and c are real numbers except a is not equal to zero?

Accepted Answer

Quadratic equation

Answer

Exponential equation

Answer

Linear equation

Answer

Cubic equation

Question 2

A quadratic equation in one variable is written in the form ax² + bx + c = 0. Which of the following is true about the values of a, b, and c?

Accepted Answer

a, b, and c are real numbers and a ≠ 0

Answer

a, b, and c are real numbers

Answer

a, b, and c are real numbers and c is a constant.

Answer

a, b, and c are any number

Question 3

Which of the following equations is a quadratic equation?

Accepted Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Question 4

In the quadratic equation

ax^2 + bx + c = 0

, what are the values of

a

,

b

, and

c

respectively?

Accepted Answer

2x^2 - 3x + 5 = 0

,

b = -6

,

c = 2

Answer

2x^2 - 3x + 5 = 0

,

b = -6

,

c = 2

Answer

2x^2 - 3x + 5 = 0

,

b = -6

,

c = 2

Answer

2x^2 - 3x + 5 = 0

,

b = -6

,

c = 2

Question 5

What is the standard form of the equation

ax^2 + bx + c = 0

?

Accepted Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Question 6

Which of the following quadratic equations can be solved easily by extracting square roots?

Accepted Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Question 7

What are the roots of the quadratic equation

ax^2 + bx + c = 0

?

Accepted Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Question 8

What are the possible values for

ax^2 + bx + c = 0

when

a

?

Accepted Answer

2x^2 - 3x + 5 = 0

or

b = -6

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Question 9

Solve the equation

ax^2 + bx + c = 0

by extracting the square roots.

Accepted Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Question 10

What are the possible solutions for m after solving the equation 2(m - 3)² + 4 = 102 correctly?

Accepted Answer

10 and -4

Answer

7 and -1

Answer

5 and 1

Answer

9 and -3

Question 11

Which of the following quadratic equations has roots of 2 and -5?

Accepted Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Question 12

When completing the square for the equation

ax^2 + bx + c = 0

, what must be added to both sides to form a perfect square?

Accepted Answer

25

Answer

30

Answer

20

Answer

15

Question 13

What must be added to x² + 10x + _____ to make it a perfect square trinomial?

Accepted Answer

25

Answer

20

Answer

30

Answer

15

Question 14

Which of the following is a perfect square trinomial?

Accepted Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Question 15

In the expression

ax^2 + bx + c = 0

, what is

a

to make the expression a perfect square?

Accepted Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Question 16

Using the quadratic formula, what are the solutions for the equation

ax^2 + bx + c = 0

?

Accepted Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Question 17

Determine the roots of the quadratic equation

ax^2 + bx + c = 0

using the quadratic formula.

Accepted Answer

x = -3 or x = -5

Answer

x = -7 or x = -1

Answer

x = -4 or x = 2

Answer

x = 3 or x = -5

Question 18

What is the value of the discriminant for the quadratic equation

ax^2 + bx + c = 0

?

Accepted Answer

12

Answer

0

Answer

20

Answer

-12

Question 19

In a quadratic equation, if the value of

ax^2 + bx + c = 0

is less than 0, what is the nature of the roots?

Accepted Answer

The roots are complex and not real (imaginary)

Answer

The roots are real and equal

Answer

The roots are real and distinct

Answer

The roots are irrational

Question 20

What does it mean for a quadratic equation's roots if the discriminant is zero,

ax^2 + bx + c = 0

?

Accepted Answer

The roots are real and equal

Answer

The roots are imaginary

Answer

The roots are complex

Answer

The roots are real and distinct

Question 21

In symbol, what represents the sum of the roots of the quadratic equation

ax^2 + bx + c = 0

?

Accepted Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Question 22

What is the product of the roots of the quadratic equation

ax^2 + bx + c = 0

in symbolic form?

Accepted Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Question 23

Which of the following is the quadratic equation with roots that have a sum of 4 and a product of -5?

Accepted Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Question 24

If a quadratic equation has a positive discriminant, what can be said about its roots?

Accepted Answer

The roots are real and distinct.

Answer

The roots are all integers.

Answer

The roots are imaginary.

Answer

The roots are complex and equal.

Question 25

What does it mean if a quadratic equation has a discriminant greater than zero but not a perfect square?

Accepted Answer

the equation has two distinct irrational roots

Answer

the equation has two distinct rational roots

Answer

the equation has one real root

Answer

the equation has two identical roots

Question 26

Which of the following represents the quadratic equation with roots 2 and -3?

Accepted Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Question 27

Given the quadratic equation

ax^2 + bx + c = 0

, find the product of the roots.

Accepted Answer

The product of the roots is

ax^2 + bx + c = 0

.

Answer

The product of the roots is

ax^2 + bx + c = 0

.

Answer

The product of the roots is

ax^2 + bx + c = 0

.

Answer

The product of the roots is

ax^2 + bx + c = 0

.

Question 28

The sum of the roots of a quadratic equation is -5 and their product is 6. What are the roots?

Accepted Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Answer

2x^2 - 3x + 5 = 0

Question 29

The sum of two numbers is 15 and the sum of their squares is 113. What are the numbers?

Accepted Answer

The numbers are 7 and 8.

Answer

The numbers are 4 and 11.

Answer

The numbers are 6 and 9.

Answer

The numbers are 5 and 10.

Question 30

The sum of two numbers is 20 and the sum of their squares is 244. What are the numbers?

Accepted Answer

The numbers are 12 and 8.

Answer

The numbers are 10 and 10.

Answer

The numbers are 13 and 7.

Answer

The numbers are 11 and 9.

Question 31

A rectangle's length is 4 meters more than its width, and it has an area of 21 m². What are its dimensions?

Accepted Answer

Length: 7 m, Width: 3 m

Answer

Length: 5 m, Width: 5 m

Answer

Length: 6 m, Width: 3 m

Answer

Length: 8 m, Width: 1 m

Question 32

The perimeter of a rectangular lot is 30 m and its area is 50 m². What equation represents the perimeter of the rectangle in lowest terms?

Accepted Answer

L + W = 15

Answer

2 (L + W) = 50

Answer

L + W = 30

Answer

2 (L + W) = 30

Question 33

In the previous problem, the perimeter of a rectangular lot is 30 m and the area is 50 m².If the equation representing the perimeter in lowest terms is $L + W = 15$ , what are the length and width of the lot?

Accepted Answer

C. 10 m and 5 m

Answer

B. 11 m and 4 m

Answer

D. 9 m and 6 m

Answer

A. 12 m and 3 m

Question 34

The perimeter of a rectangular garden is 28 meters, and the area is 48 square meters.What are the dimensions of the garden?

Choices:

Accepted Answer

D. 8 m and 6 m

Answer

B. 9 m and 5 m

Answer

A. 10 m and 4 m

Answer

C. 12 m and 2 m

Question 35

The sum of two numbers is 12, and the sum of their squares is 74. Find the numbers.

Accepted Answer

The numbers are 5 and 7

Answer

The numbers are 6 and 6

Answer

The numbers are 4 and 8

Answer

The numbers are 3 and 9

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