Chapter 3:Pair of Linear Equations in Two Variables

Chapter 5: Arithmetic Progression

Chapter 8: Introduction to Trigonometry

Chapter 9:Some Applications of Trigonometry

Chapter 12:Area Related to Circles

Quadratic Equations

(i) (x + 1)

(ii) x

(iii) (x – 2)(x + 1) = (x – 1)(x + 3)

(iv) (x – 3)(2x +1) = x(x + 5)

(v) (2x – 1)(x – 3) = (x + 5)(x – 1)

(vi) x

(vii) (x + 2)

(viii) x

(x + 1)

(a+b)

⇒ x

⇒ x

which is form of ax

It is a quadratic equation.

(ii) Given,

x

⇒ x

⇒ x

which is form of ax

It is quadratic equation.

(iii) Given,

(x – 2)(x + 1) = (x – 1)(x + 3)

⇒ x

It is not a quadratic equation.

(iv) Given,

(x – 3)(2x +1) = x(x + 5)

⇒ 2x

⇒ x

which is form of ax

It is quadratic equation.

(v) Given,

(2x – 1)(x – 3) = (x + 5)(x – 1)

⇒ 2x

⇒ x

It is form of ax

where a ≠ 0, and b,c are any real number

It is quadratic equation.

(vi) Given,

x

⇒ x

⇒ 7x – 3 = 0

It is form of ax

where a=0 and b,c are any real number

It is not a quadratic equation.

(vii) Given,

(x + 2)3 = 2x(x2 – 1)

⇒ x

⇒ x3 + 14x – 6x2 – 8 = 0

It is not in the form of ax

It is not a quadratic equation.

(viii) Given, x

2x

It is the form of ax

where a ≠ 0, and b,c are any real number

It is quadratic equation.

(i) The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

(ii) The product of two consecutive positive integers is 306. We need to find the integers.

(iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken

Thus, the length of the plot = (2x + 1) m

Area of rectangle = length × breadth

(2x + 1)x = 528

2x

2x

which is of the form of ax

where a ≠ 0, and b,c are any real number

It is represent the required quadratic equation.

(ii) Let The first integer number = x

Thus, the next consecutive positive integer will be = x + 1

According to the question

Product of two consecutive integers = x X (x +1) = 306

x

x

It is of the form of ax

where a ≠ 0, and b,c are any real number

It is represent the required quadratic equation.

.

(iii) Let Age of Rohan’s = x years

Rohan’s mother’s age = x + 26

After 3 years,

Age of Rohan’s = x + 3

Age of Rohan’s mother will be = x + 26 + 3 = x + 29br> According to question

(x + 3)(x + 29) = 360

x

x

x

which is of the form of ax

where a ≠ 0, and b,c are any real number

It is represent the required quadratic equation.

(iv) Let us consider, The speed of train = x km/h

Time taken to travel 480 km = 480/x km/hr

speed of train = (x – 8) km/h

Therefore, time taken to travel 480 km =

480
/
(x-8)

km/hAccording to the question

Speed × Time = Distance (

480
/
(x-8)

)
- (
480
/
x

)=3(

480x-480(x-8)
/
x(x-8)

)=3480x - 480x +3840 =3x(x-8)

3840= 3x

3x

x

x

which is of the form of ax

where a ≠ 0, and b,c are any real number

It is represent the required quadratic equation.

.