Quadratic Equations Revision
Quadratic Equations Revision
Part A: Solve the Following Quadratic Problems
Solve: \( x^2 - 5x + 6 = 0 \)
Factorize: \( x^2 + 2x - 8 \)
Solve using the quadratic formula: \( 2x^2 - 3x - 5 = 0 \)
Solve by completing the square: \( x^2 + 4x - 1 = 0 \)
Find the roots of \( x^2 - 16 = 0 \)
Solve: \( x^2 - 2x = 0 \)
If \( x^2 + 6x + 9 = 0 \), find \( x \)
Solve for \( x \): \( 3x^2 + x - 2 = 0 \)
Factor completely: \( x^2 - x - 12 \)
Find the roots: \( x^2 = 7x \)
Find the discriminant of \( x^2 - 4x + 3 = 0 \)
Find the nature of the roots of \( x^2 + 4x + 5 = 0 \)
Solve: \( 5x^2 = 20 \)
Solve: \( x^2 + 2x = 0 \)
Find two numbers whose product is 12 and sum is 7.
Factor: \( 4x^2 - 25 = 0 \)
Solve: \( x^2 - 3x + 2 = 0 \)
Find the roots of \( x^2 - 10x + 25 = 0 \)
Solve: \( x^2 + 5x = -6 \)
Solve using quadratic formula: \( x^2 + 2x + 3 = 0 \)
Solve: \( 2x^2 - 4x = 0 \)
Solve: \( x^2 = 9 \)
Solve: \( x^2 + 3x = 10 \)
Find the sum and product of roots of \( x^2 - 6x + 9 = 0 \)
Solve: \( x(x + 7) = 0 \)
Factorize: \( x^2 - 81 \)
Find the roots: \( x^2 + 2x - 15 = 0 \)
Solve: \( 4x^2 + 4x + 1 = 0 \)
Find values of \( x \) for which \( x^2 - 4x = -4 \)
If \( x^2 + bx + 16 = 0 \) has equal roots, find \( b \)
Part B: Word Problems
The product of two consecutive integers is 132. Find the integers.
A rectangular garden has an area of 120 m². Its length is 4 meters more than its width. Find the dimensions.
The sum of a number and its square is 30. Find the number.
The height of a triangle is 3 cm less than its base. If the area is 54 cm², find the base and height.
A person can row 12 km downstream and 8 km upstream in the same time. The speed of the stream is 2 km/h. Find the speed of the boat in still water.
A pen and a book together cost $30. The price of the book is $4 more than twice the pen. Find the price of each.
The square of a number is equal to 5 times the number. Find the number.
The difference between a number and its reciprocal is 2. Find the number.
A train travels a certain distance in 5 hours. If its speed was 6 km/h faster, it would take 1 hour less. Find the distance.
The width of a rectangle is 5 m less than its length. If the area is 84 m², find its dimensions.
The height of a cone is twice its radius. If the volume is \( 376.99 \text{ cm}^3 \), find the radius. Use \( \pi = 3.14 \).
A man is 4 times as old as his son. In 5 years, he will be 3 times as old. Find their ages.
A number is divided into two parts such that the square of one exceeds the other by 24. Find the number.
One leg of a right triangle is 7 cm more than the other. The hypotenuse is 13 cm. Find the lengths of the legs.
The perimeter of a rectangle is 34 cm. If its area is 60 cm², find its dimensions.
A number is such that when it is added to its square, the result is 72. Find the number.
Twice the square of a number is 50 more than the number. Find the number.
The product of a number and one less than itself is 132. Find the number.
The area of a square plot is numerically equal to 4 times its perimeter. Find the side length.
A rectangular field is 20 meters longer than it is wide. If its area is 1200 m², find its dimensions.
Show/Hide Answers
Answers
\( x = 2, 3 \)
\( (x + 4)(x - 2) \)
\( x = 2, -\frac{5}{2} \)
\( x = -2 \pm \sqrt{5} \)
\( x = \pm4 \)
\( x = 0, 2 \)
\( x = -3 \) (double root)
\( x = \frac{2}{3}, -1 \)
\( (x - 4)(x + 3) \)
\( x = 0, 7 \)
\( D = 4 \)
Complex roots
\( x = \pm2 \)
\( x = 0, -2 \)
\( x = 3, 4 \)
\( x = \pm\frac{5}{2} \)
\( x = 1, 2 \)
\( x = 5 \)
\( x = -6, 1 \)
No real roots
\( x = 0, 2 \)
\( x = \pm3 \)
\( x = 2, -5 \)
Sum = 6, Product = 9
\( x = 0, -7 \)
\( (x - 9)(x + 9) \)
\( x = 3, -5 \)
\( x = -\frac{1}{2} \)
\( x = 2 \)
\( b = \pm8 \)
11 and 12
Width = 10 m, Length = 14 m
5
Base = 12 cm, Height = 9 cm
Speed = 10 km/h
Pen = $8, Book = $22
0 or 5
2 or -1
Distance = 120 km
Width = 7 m, Length = 12 m
Radius = 3.5 cm
Father = 40, Son = 10
Parts = 6 and 18
Legs = 5 cm and 12 cm
Length = 10 cm, Width = 7 cm
8
5
12
Side = 16
Width = 30 m, Length = 50 m
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