Question 1

Which of the following equations illustrates a quadratic equation?

Accepted Answer

(x+3) (x-10) = 0

Answer

(4x+5) (10) = 90

Answer

(x+3) (x+2) = x² + 2

Answer

2x²+5x+10 = 2x²

Question 2

Which of the following shows the standard form of this quadratic equation: 15 + 4x² = 2x² – 3x?

Accepted Answer

2x² + 3x + 15 = 0

Answer

2x² – 3x – 15 = 0

Answer

2x² – 3x + 15 = 0

Answer

2x² + 3x – 15 = 0

Question 3

In the equation (x+4) (x-2) = 0, which of the statement best explains why it is considered quadratic?

Accepted Answer

It is a product of two binomials, when expanded, results in a second-degree polynomial.

Answer

It is an equation that can be solved without factoring.

Answer

It contains only one variable raised to the first power.

Answer

It represents a linear relationship between two variables.

Question 4

Which of the following equations best matches the statement below?

“This equation is quadratic because it contains a variable raised to the second power and can be written in the format ax² + bx + c = 0.”

Accepted Answer

3x² + 5x – 2 = 0

Answer

2(x + 1) = 2x + 2

Answer

4x – 7 = 0

Answer

x³ + x = 0

Question 5

Solve the equation using extracting square roots: x² = 49.

Accepted Answer

x = <math>\pm7</math>

Answer

x = <math>\pm49</math>

Answer

x = 7

Answer

x = 0

Question 6

Solve the equation using factoring: x²– 5x + 6 = 0.

Accepted Answer

x = 2 or x = 3

Answer

x = -2 or x = -3

Answer

x = -1 or x = -6

Answer

x = 1 or x = 6

Question 7

Solve the equation by completing the square: x²+ 6x + 5 = 0.

Accepted Answer

x = -3 $\pm7$

Answer

x = -3 $\pm7$

Answer

x = -2 $\pm7$

Answer

x = -1 or x = -5

Question 8

Solve using the quadratic formula: 2x²+ 3x – 2 = 0.

Accepted Answer

$x=\frac{-3\pm\sqrt{25}}{4}$

Answer

$x=\frac{-3\pm\sqrt{25}}{4}$

Answer

$x=\frac{-3\pm\sqrt{25}}{4}$

Answer

$x=\frac{-3\pm\sqrt{25}}{4}$

Question 9

Solve the equation using extracting square roots: 4x² = 100

Accepted Answer

$x=\frac{-3\pm\sqrt{25}}{4}$

Answer

$x=\frac{-3\pm\sqrt{25}}{4}$

Answer

$x=\frac{-3\pm\sqrt{25}}{4}$

Answer

$x=\frac{-3\pm\sqrt{25}}{4}$

Question 10

Solve the equation using factoring: x²+ 2x – 8 = 0.

Accepted Answer

x = 2 or x = -4

Answer

x = -1 or x = 8

Answer

x = -4 or x = -2

Answer

x = 4 or x = -2

Question 11

Solve the equation by completing the square: x²– 4x + 1 = 0.

Accepted Answer

$x=\frac{-3\pm\sqrt{25}}{4}$

Answer

$x=\frac{-3\pm\sqrt{25}}{4}$

Answer

$x=\frac{-3\pm\sqrt{25}}{4}$

Answer

$x=\frac{-3\pm\sqrt{25}}{4}$

Question 12

Solve the equation using the quadratic formula: x² – 2x – 3 = 0.

Accepted Answer

$x=\frac{-3\pm\sqrt{25}}{4}$

Answer

$x=\frac{-3\pm\sqrt{25}}{4}$

Answer

$x=\frac{-3\pm\sqrt{25}}{4}$

Answer

$x=\frac{-3\pm\sqrt{25}}{4}$

Question 13

Find the discriminant value of the quadratic equation 2x² + 7x – 6 = 0?

Accepted Answer

97

Answer

D = 1

Answer

-97

Answer

D = -1

Question 14

Which of the following equation has a discriminant value of -35?

Accepted Answer

x² + x + 9 = 0

Answer

x² + 5x – 6 = 0

Answer

2x² + 3x + 4 = 0

Answer

x² + 3x – 4 = 0

Question 15

What is the discriminant value of the quadratic equation x² + 9x + 8 = 0?

Accepted Answer

D = 49

Answer

113

Answer

-113

Answer

-49

Question 16

Which of the following equation has a discriminant value of -23?

Accepted Answer

2x² + 3x + 4 = 0

Answer

x² + 5x – 6 = 0

Answer

x² + x + 9 = 0

Answer

x² + 3x – 4 = 0

Question 17

Determine the nature of the roots of the quadratic equation x² + 6x – 9 = 0?

Accepted Answer

The roots are real and equal.

Answer

The roots are rational and not equal.

Answer

The roots are irrational and not equal.

Answer

There are no real roots.

Question 18

Determine the nature of the roots of the quadratic equation x² + x + 9 = 0?

Accepted Answer

There are no real roots.

Answer

The roots are real and equal.

Answer

The roots are irrational and not equal.

Answer

The roots are rational and not equal.

Question 19

Determine the nature of roots of the quadratic equation x² + 4x + 4 = 0?

Accepted Answer

The roots are real and equal.

Answer

There are no real roots.

Answer

The roots are rational and not equal.

Answer

The roots are irrational and not equal.

Question 20

Determine the nature of roots of the quadratic equation x² + 5x – 3 = 0?

Accepted Answer

The roots are irrational and not equal.

Answer

The roots are real and equal.

Answer

There are no real roots.

Answer

The roots are rational and not equal.

Question 21

In the quadratic equation x² + 6x + 9= 0, find the sum and product of its roots.

Accepted Answer

S = -6 and P = 9

Answer

S = 6 and P = 9

Answer

S = 9 and P = 6

Answer

S = 9 and P = -6

Question 22

In the equation 3x² + 12x + 30 = 0, find its sum and product of roots.

Accepted Answer

S = -4 and P = 10

Answer

S = 10 and P = -4

Answer

S = 4 and P = 10

Answer

S = 10 and P = 4

Question 23

In the quadratic equation x² + 2x – 8= 0, it has roots that adds up to -2 and when multiplied is –8. What are the roots of this equation?

Accepted Answer

2 and – 4

Answer

– 4 and – 2

Answer

– 2 and 4

Answer

8 and – 1

Question 24

If a quadratic equation has roots that sum to 7 and a product to 10, what are the roots?

Accepted Answer

2 and 5

Answer

3 and 4

Answer

5 and 7

Answer

1 and 10

Question 25

If the sum of the roots of a quadratic equation is 5 and the product is 6, which equation represents this relationship?

Accepted Answer

x² – 5x + 6 = 0

Answer

x² – 6x + 5 = 0

Answer

x² + 5x + 6 = 0

Answer

x² + 6x – 5 = 0

Question 26

What is the quadratic equation of whose roots are – 2 and 5?

Accepted Answer

x² – 3x – 10 = 0

Answer

x² – 2x + 5 = 0

Answer

x² + 2x – 5 = 0

Answer

x² + 3x – 10 = 0

Question 27

If the roots of a quadratic equation are 1 and –8, what is the equation?

Accepted Answer

x² + 7x – 8 = 0

Answer

x² – 8x + 1 = 0

Answer

x² + 8x – 1 = 0

Answer

x² – 7x – 8 = 0

Question 28

If the roots of a quadratic equation are ½ and -3, what is the equation?

Accepted Answer

2x² + 5x – 3 = 0

Answer

2x² – 5x – 3 = 0

Answer

2x²– x – 3 = 0

Answer

2x² – x + 3 = 0

Question 29

Find the roots of the equation x (x + 3) = 40.

Accepted Answer

– 8&#44; 5

Answer

– 5&#44; 8

Answer

– 10&#44; 4

Answer

– 4&#44; 10

Question 30

Find the roots of the equation x (x – 4) = 21.

Accepted Answer

7&#44; – 3

Answer

– 7, – 3

Answer

– 7&#44; 3

Answer

7&#44; 3

Question 31

Find the roots of the equation r (r + 12) = – 27.

Accepted Answer

– 9&#44; 3

Answer

– 3&#44; 9

Answer

– 6, – 3

Answer

– 3, – 9

Question 32

Find the roots of the equation g (g – 2) = 15.

Accepted Answer

– 3&#44; 5

Answer

– 3, – 5

Answer

3&#44; 5

Answer

– 5&#44; 3

Question 33

Transform the equation $\pm7$ into quadratic equation.

Accepted Answer

x² – 7x + 12 = 0

Answer

x² + 7x – 12 = 0

Answer

x² – 7x – 18 = 0

Answer

x² + 7x – 21 = 0

Question 34

Transform the equation into $\pm7$ quadratic equation.

Accepted Answer

x² – 9x + 10 = 0

Answer

x² – 9x – 10 = 0

Answer

x² + 10x – 9 = 0

Answer

x² + 9x – 10 = 0

Question 35

Using the equation x²-7x+12 = 0, what will be the roots of the quadratic equation?

Accepted Answer

4&#44; 3

Answer

– 4, – 3

Answer

4&#44; – 3

Answer

– 4&#44; 3

Question 36

Find the roots of the equation $\pm7$ .

Accepted Answer

6&#44; 1

Answer

– 6&#44; 1

Answer

– 6, – 1

Answer

– 1&#44; 6

Question 37

A rectangular parking lot has an area of 120 m²and a perimeter of 46 m. What are its length and width?

Accepted Answer

Length = 15 m, Width = 8 m

Answer

Length = 18 m, Width = 8 m

Answer

Length = 16 m, Width = 7.5 m

Answer

Length = 20 m, Width = 6 m

Question 38

A rectangular swimming pool has an area of 96 m²and a perimeter 40 m. What are its length and width?

Accepted Answer

Length = 12 m, Width = 8 m

Answer

Length = 10 m, Width = 9.6 m

Answer

Length = 16 m, Width = 6 m

Answer

Length = 14 m, Width = 6 m

Question 39

The length of a banner is 4 m more than twice its width, and its area is 160 m². What is the length of the banner?

Accepted Answer

20 m

Answer

22 m

Answer

24 m

Answer

26 m

Question 40

The length of a billboard is 5 m more than twice its width, and its area is 210 m². What is the length of the billboard?

Accepted Answer

15 m

Answer

16 m

Answer

14 m

Answer

12 m

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