Solve (x 3)(x + 8) = 0



Chapter 1 Quadratic Equations in One Unknown (I)

Question 1

Solve (x ( 3)(x + 8) = 0.

A. x = (3 or 8

B. x = ( 8 or 3

C. x = ( 8 or ( 3

D. x = 3 or 8

Answer: B

Skill: Factor Method

Solution

[pic]

Question 2

The roots of [pic] are and .

Answer: -2, 5 or 5, -2

Skill: Factor Method

Solution

[pic]

∴ The roots of (2 + x)((x + 5) = 0 are (2 and 5.

Question 3

Solve [pic].

A. [pic] or −6

B. [pic] or 23

C. [pic] or −9

D. No real roots

Answer: C

Skill: Factor Method

Solution

[pic]

Question 4

Solve [pic].

A. [pic] or −9

B. [pic]

C. [pic]

D. [pic] or 9

Answer: A

Skill: Factor Method

Solution

[pic]

Try a similar problem:

Solve x(x + 2) = 3.

A. x = –1 or –3

B. x = 1 or –3

C. x = –1 or 3

D. x = 1 or 3

Answer: B

Skill: Factor Method

Solution

[pic]

Question 5

The roots of [pic] are and .

Answer: -11, 2 or 2, -11

Skill: Factor Method

Solution

[pic]

∴ The roots of x2 + 9x – 22 = 0 are (11 and 2.

Question 6

Solve 2x2 ( x (2 = 0.

A. x =[pic] or [pic]

B. x = [pic] or [pic]

C. x = [pic] or [pic]

D. x = [pic] or [pic]

Answer:A

Skill: Quadratic Formula

Solution

2x2 – x – 2 = 0

Using the quadratic formula,

[pic]

Question 7

Solve [pic].

A. [pic] or [pic]

B. [pic] or [pic]

C. [pic] or [pic]

D. [pic] or [pic]

Answer: B

Skill: Quadratic Formula

Solution

[pic]

Using the quadratic formula,

[pic]

Question 8

Which of the following are NOT the roots of [pic]?

I. [pic]

II. [pic]

III. [pic]

A. I and II only

B. II and III only

C. I and III only

D. I, II and III

Answer: B

Skill: Quadratic Formula

Solution

2x2 – 3x – 3 = 0

Using the quadratic formula,

[pic]

∴ [pic] are not the roots of 2x2 – 3x – 3 = 0.

Question 9

Solve [pic].

A. [pic] or [pic]

B. [pic] or [pic]

C. [pic] or [pic]

D. [pic] or [pic]

Answer: A

Skill: Quadratic Formula

Solution

[pic]

Using the quadratic formula,

[pic]

Try a similar problem:

Solve 7x2 = 6x + 3.

A. [pic]

B. [pic]

C. [pic]

D. [pic]

Answer: C

Skill: Quadratic Formula

Solution

[pic]

Using the quadratic formula,

[pic]

Question 10

The roots of [pic] are and . (Give your answers correct to 2 significant figures)

Answer: 0.19, -5.2 or -5.2, 0.19

Skill: Quadratic Formula

Solution

x2 + 5x – 1 = 0

Using the quadratic formula,

[pic]

Question 11

Solve the quadratic equation ax2 + bx + c = 0 using the graph below.

[pic]

A. [pic] or 2.5

B. [pic] or 1

C. [pic] or (1

D. [pic] or (2

Answer: B

Skill: Graphical Method

Solution

The x-intercepts of the graph of y = ax2 + bx + c are (2.5 and 1.

Therefore, the roots of ax2 + bx + c = 0 are (2.5 and 1.

Try a similar problem:

Find the y-intercept of the given quadratic graph shown in the figure.

[pic]

A. (8

B. (9

C. (10

D. (11

Answer: C

Skill: Graphical Method

Solution

∵ The x-intercepts of the given graph are (5 and 2.

∴ The given graph is

[pic]

∴ The y-intercept of the given graph is (10.

Question 12

From the graph below, the root of [pic] is .

[pic]

Answer: 1.5

Skill: Graphical Method

Solution

The x-intercept of the graph of y = 4x2 – 12x + 9 is 1.5.

Therefore, the root of 4x2 – 12x + 9 = 0 is 1.5.

Question 13

The following shows the graph of [pic].

[pic]

How many real roots does the equation [pic] have?

A. 0

B. 1

C. 2

D. Cannot be determined.

Answer: A

Skill: Graphical Method

Solution

∵ The graph of y = px2 + qx + r has no x-intercept.

∴ The equation px2 + qx + r = 0 has no real root.

Question 14

From the graph below, the equation [pic] has real roots. (Input the numbers 0, 1 or 2.)

[pic]

Answer: 2

Skill: Graphical Method

Solution

[pic]

∵ The graph of y = (2x2 + 4x + 3 has two x-intercepts.

∴ The equation 2x2 – 4x – 3 = 0 has two real roots.

Question 15

Form a quadratic equation in x whose roots are greater than the roots of [pic]by 1.

A. 2x2 + 7x + 9 = 0

B. x2 + 3x + 7 = 0

C. x2 + 11x + 18 = 0

D. x2 ( 2x ( 15 = 0

Answer: D

Skill: Forming Quadratic Equation

Solution

[pic]

∴ The roots of the required equation are (4 +1 and 4 + 1, i.e. (3 and 5.

∵ [pic]

∴ [pic]

∴ [pic]

∴ The required equation is x2 – 2x – 15 = 0.

Try a similar problem:

Form a quadratic equation in x whose roots are greater than the roots of

(x – 3)(x + 1) = 0 by 2.

A. x2 ( 6x + 5 = 0

B. x2 + 6x + 5 = 0

C. x2 + 6x ( 5 = 0

D. x2 ( 6x ( 5 = 0

Answer: A

Skill: Forming Quadratic Equation

Solution

[pic]

∴ The roots of the required equation are 3 + 2 and (1 +2, i.e. 5 and 1.

∵ [pic]

∴ [pic]

∴ The required equation is x2 – 6x + 5 = 0.

Question 16

Which of the following quadratic equations has roots [pic] and 2?

A. [pic]

B. [pic]

C. [pic]

D. [pic]

Answer: A

Skill: Forming Quadratic Equation

Solution

The required quadratic equation is

[pic]

Question 17

If the roots of [pic] are [pic] and 3, then [pic] .

Answer: -7

Skill: Forming Quadratic Equation

Solution

The required quadratic equation is

[pic]

∴ [pic]

Question 18

Form a quadratic equation in x whose roots are the reciprocals of the roots of [pic].

A. [pic]

B. [pic]

C. [pic]

D. [pic]

Answer: C

Skill: Forming Quadratic Equation

Solution

[pic]

∴ The roots of the required equation are [pic] and [pic], i.e. [pic] and [pic].

∵ [pic]

[pic]

∴ The required equation is 6x2 + 5x + 1 = 0.

Question 19

The product of two consecutive positive integers is 132. Then the larger integer is

.

Answer: 12

Skill: Application of Quadratic Equation

Solution

Let x be the larger integer, then x – 1 is the smaller integer.

[pic]

∴ The larger integer is 12.

Question 20

The product of two consecutive positive odd numbers is 63. Then the smaller number is .

Answer: 7

Skill: Application of Quadratic Equation

Solution

Let x be the smaller number, then x + 2 be the larger number.

[pic]

∴ The smaller number is 7.

Try a similar problem:

The product of two consecutive positive even numbers is 80. Then the larger number is .

Answer: 10

Skill: Application of Quadratic Equation

Solution

Let x be the larger number, then x – 2 be the smaller number.

[pic]

∴ The larger number is 10.

Question 21

The figure shows a right prism with square base of length x cm. If the height of the prism is 10 cm and the total surface area is 138 cm2, find the value of x.

[pic]

A. 2

B. 3

C. 4

D. 5

Answer: B

Skill: Application of Quadratic Equation

Solution

Total surface area = 138 cm2

[pic]

Question 22

The square of the difference between a number and 6 is equal to the number itself. Then the number is or .

Answer: 9, 4 or 4, 9

Skill: Application of Quadratic Equation

Solution

Let x be the number.

[pic]

∴ The number is 9 or 4.

Question 23

In the figure, the area of △ABC is 30 cm2 and [pic]. Find the value of x.

[pic]

A. 10

B. 8

C. 6

D. 4

Answer: A

Skill: Application of Quadratic Equation

Solution

Area of △ABC = 30 cm2

[pic]

Question 24

In the figure, ABCD is a trapezium with area 24 cm2. Then [pic] .

[pic]

Answer: 4

Skill: Application of Quadratic Equation

Solution

Area of trapezium ABCD = 24 cm2

[pic]

Question 25

Tom is one year older than Kelvin. If the product of their ages is 272, Tom is

years old.

Answer: 17

Skill: Application of Quadratic Equation

Solution

Let x be the age of Tom, then x – 1 is the age of Kelvin.

[pic]

∴ Tom is 17 years old.

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[pic]

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