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Quadratic Equations Video Questions and Answers
Use completing the square method to solve
3
x
2
+
8
x
-
6
=
0
, correct to 3 significant figures.
(4m 12s)
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1.
The length of a rectangular mat is
1
1
2
m
longer than its width. Find the length of the mat if its area is
4
1
2
m
2
2.
The sum of two numbers is 24. The difference of their squares is 144. What are the two numbers?
3.
Find the coordinates of the points of intersection of the straight line x-y=5 and the hyberbola xy=9
4.
Solve for x:
2
x
2
+
x
-
36
=
0
5.
Solve the simultaneous equations
x
2
+
y
2
=
26
, x-y=4
6.
When the price of an item was increased by sh.5, 1 bought 2 items fewer with sh.200. What is the current price of the item?
7.
Solve the simultaneous equations 2x-y=3,
x
2
-
x
y
=
-
4
8.
The length of a room is 4 metres longer than its width. Find the length of the room if its area is
32
m
2
9.
The length of a rectangle is (3x+1) cm. Its width is 3 cm shorter than its length. Given that the area of the rectangle is
28
c
m
2
, find its length.
10.
A retailer planned to buy some computers from a total of sh 1,800,000. Before the retailer could buy the computers the price per unit was reduced by sh.4,000. This reduction in price enabled the retailer to buy five more computers using the same amount of money as originally planned. (a) Determine the number of computers the retailer bought. (b) Two of the computers purchased got damaged while in
11.
The length of a flower garden is 2m less than twice its width. The area of the garden is
60
m
2
. Calculate its length.
12.
(a) Express
1
x
-
2
-
2
x
+
5
=
3
x
+
1
in the form of
a
x
2
+
b
x
=
0
, where a, b, and c are constants hence solve for x. (b) Neema did y tests and scored a total of 120 marks. She did two more tests which she scored 13 and 14 marks. The mean score of the first y tests was 3 marks more than the mean score for all the tests she did. Find the total number of tests that she did.
13.
Solve the equations. x+y =17, xy-5x=32
14.
(a) Solve the equation,
x
+
3
24
=
1
x
-
2
(b) The length of a floor of a rectangular hall is 9 m more than its width. The area of a floor is
136
m
2
. (i) Calculate the perimeter of the floor. (ii) A rectangular carpet is placed on the hall leaving an area of
64
m
2
. If the length of the carpet is twice its width, determine the width of the carpet.
15.
A cow is 4 years 8 months older than a heifer. The product of their ages is 8 years. Determine the age of the cow and that of the heifer.
16.
Solve the simultaneous equations; 3x-y=9,
x
2
-
x
y
=
4
17.
The length and width of a rectangular signboard are (3x+12) and (x-4) respectively .If the diagonal of the signboard is 200 cm, determine its area.
18.
The roots of a quadratic equation are
x
=
-
3
5
and x = 1. Form the quadratic equation in the form
a
x
2
+
b
x
+
c
=
0
where a, b and c are integers.
19.
Use completing the square method to solve
3
x
2
+
8
x
-
6
=
0
, correct to 3 significant figures.
20.
Solve the equations. x + 3y = 13,
x
2
+
3
y
2
=
43
21.
A group of people planned to contribute equally towards a water project which needed Ksh.2,000,000 to complete. However, 40 members of the group withdrew from the project. As a result, each of the remaining member was to contribute Ksh.2,500 more. (a) Find the original number of members in the group. (b)Forty five percent of the value of the project was funded by the Constituency Development..
22.
A school planned to buy x calculators for a total cost of Ksh 16,200. The supplier agreed to offer a discount of Ksh 60 per calculator. The school was then able to get three extra calculators for the same amount of money. (a) Write an expression in terms of x, for the: (i) Original price of each calculator; (ii) Price of each calculator after the discount (b) Form an equation in x and hence
23.
A quadratic curve passes through the points ( -2,0) and (1,0). Find the equation of the curve in the form y =ax2+bx+c, where a, b and c are constants.
24.
Motorbike A travels at 10km/h faster than motorbike B whose speed is x km/h. Motorbike A takes
1
1
2
hours less than motorbike B to cover a 180 km journey. (a) Write an expression in terms of x for the time taken to cover the 180km journey by: (i) Motorbike A; (ii) (ii) Motorbike B. (b) Use the expression in (a) above to determine the speed, in km/h, of motorbike A. (c) For a journey of 48km
25.
A hall can accommodate 600 chairs arranged in rows. Each row has the same number of chairs. The chairs are rearranged such that the number of rows are increased by 5 but the number of chairs per row is decreased by 6. (a) Find the original number of rows of chairs in the hall. (b) After the rearrangements 450 people were seated in the hall leaving the same number of empty chairs in each row.
26.
An institution intended to buy a certain number of chairs for Ksh.16 200. The supplier agreed to offer a discount of Ksh 60 per chair which enabled the institution to get 3 more chairs. Taking x as the originally intended number of chairs, (a) Write an expression in terms of x for: (i) Original price per chair (ii) Price per chair after discount (b) Determine: (i) The number of chairs the
27.
The length of a room is 3 m shorter than three times its width. The height of the room is a quarter of its length. The area of the floor is 60 m2. (a) Calculate the dimensions of the room. (b) The floor of the room was tiled leaving a border of width y m, all round. If the area of the border was 1.69 m2, find: (i) The width of the border; (ii) The dimensions of the floor area covered by tiles.
28.
A photograph print measuring 24 cm by 15 cm is enclosed in a frame. A uniform space of width x cm is left in between the edges of the photograph and the frame. If the area of the space is
270
c
m
2
, find the value of x.
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