WBBSE Solutions For Class 10 Maths Chapter 1 Quadratic Equations In One Variable Exercise 1.3

WBBSE Maths Class 10 Chapter 1 Quadratic Equations In One Variable Exercise 1.3

Question 1: The difference between two positive whole numbers is 3 and the sum of their squares is 117 by calculating, let us write the two numbers.

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Wbbse Class 10 Solutions Quadratic Equation With One Variable Question 2:

The base of a triangle is 18m. more than two times its height, if the area of the triangle is 360 sq.m, then let us determine its height of it.

WBBSE Maths Class 10

Wbbse Class 10 Solutions Quadratic Equation With One Variable Question 3:

If 5 times of a positive whole number is less by 3 than twice of its square, then let us determine the number.

Wbbse Class 10 Solutions Quadratic Equation With One Variable Question 4:

The distance between two places is 200 km; the time taken by a motor car from one place to another is less by 2 hrs. than the time taken by a Jeep car. If the speed of the motor car is 5 km/hr. more than the speed of the Jeep car, then by calculating let us write the speed of the motor car.

Wbbse Class 10 Maths Chapter 1 Exercise 1.3 Question 5:

The area of Amita’s rectangular land is 2000 sq.m and the perimeter of it is 180 m. By calculating, let us write the length and breadth of the Amita’s land.

 

Wbbse Class 10 Maths Chapter 1 Exercise 1.3 Question 6:

The tens digit of a two-digit number is less by 3 than the unit digit. If the product of the two digits is subtracted from the number, the result is 15, let us write the unit digit of the number by calculation.

Wbbse Class 10 Maths Chapter 1 Exercise 1.3 Question 7:

There are two pipes in the water reservoir of our school. Two pipes together take 11 1/9 minutes to fill the reservoir. If the two pipes are opened separately, then one pipe would take 5 minutes more time than the other pipe. Let us write by calculating the time taken to fill the reservoir separately by each of the pipes.

Question 8: Porna and Pijush together complete a work in 4 days. If they work separately, then the time taken by Porna would be 6 days more than the time taken by Pijush. Let us write by calculating the time taken by Porna alone to complete the work.

Question 9: If the price of 1 dozen pens is reduced by Rs. 6, then 3 more pens will be purchased in Rs. 30. Before the reduction of price, let us calculate the price of 1 dozen pen.

 

WBBSE Class 10 Quadratic Equation In One Variable Exercise 1.3 Multiple Choice Questions

Question 1. The number of roots in a quadratic equation is

1. One

2. Two

3. Three

4. None of them

Answer: 2. Two

Question 2. If ax² + bx + c is a quadratic equation then

1. b + 0

2. c + 0

3. a + 0

4. None of these

Answer: 3. a + 0

Question 3. The highest power of the variable of a quadratic equation is

1. 1

2. 2

3. 3

4. None of these

Answer: 2. 2

Question 4. The equation 4 (5x²-7x+2) = 5 (4x²-6x + 3) is

1. Linear

2. Quadratic

3. 3rd degree

4. None of these

Answer: 1. Linear

Question 5. The root/roots of equation, x²/x = 6 are:

1. 0

2. 6

3. 0 & 6

4. -6

Answer: 3. 0 & 6

Chapter 1 Quadratic Equations In One Variable Exercise 1.3 True or False

Question 1. (x-3)²= x²-6x + 9 it is a quadratic equation

Answer: False

Question 2. Equation x² = 25 has only one root (s)

Answer: False

Chapter 1 Quadratic Equations In One Variable Exercise 1.3 Let Us Fill In The Blank :

1. If a = 0 & b + 0, in the equation ax² + bx + c = 0, then the equation is a Linear equation.

2. If the two roots of a quadratic equation are equal and equal to 1, then the equation is    x² – 2x + 1 = 0.

3. The two roots of the x²-6x are   0   &   6

WBBSE Class 10 Quadratic Equation In One Variable

Chapter 1 Quadratic Equations In One Variable Exercise 1.3 Short Answers

Question 1. Let us find the value of an if one root of equation x² + ax + 3 = 0 is 1.

Solution: If x² + ax + 3 = 0 has one root = 1,

the other root is 12+ a.1 +3 = 0

⇒ a+ 4 = 0

⇒  a = -4

WBBSE Class 10 Quadratic Equation In One Variable  Question 2.

Let us find the value of the other root if one root of the equation x² – (2 + b) x + 6 = 0 is 2.

Solution: If one root of x² – (2 + b) x + 6 = 0 is 2, the other root

⇒ (2)²– (2+b) 2+6= 0

⇒ 4-4-2b+6=0

⇒ 2b = 6

⇒ b = 3

The other root = 3.

WBBSE Class 10 Quadratic Equation In One Variable  Question 3.

Let us write the value of the other root if one root of equation 2x² + kx + 4 = 0 is 2.

WBBSE Class 10 Quadratic Equation In One Variable  Question 4.

Let us write the equation if the difference between a proper fraction and its reciprocal is 9/20

WBBSE Class 10 Quadratic Equation In One Variable  Question 5.

Let us write the values of a and b if the two roots of the equation ax² + bx +35 = 0 are -5 and -7.

WBBSE Class 10 Chapter 1 Quadratic Equations In One Variable Application

Application 1. By another method, I determine the two roots of the quadratic equation 5x² + 23x+12= 0, multiplying the left-hand side and right-hand side of it by 5 with the help of the method of completing the square.

 

Application 2: Let us check whether the two obtained values of x, that is, x = 10 and x = -7 satisfy the quadratic equation (1) or not.

Application 3: The product of two consecutive positive odd numbers is 143. Let me construct the equation and write the two odd numbers by applying Sreedhar Acharyya’s formula. 

Application 4. If the following quadratic equations have real roots, then let us determine their roots by applying Sreedhar Acharyya’s formula.

1. 1- x = 2x²

2. 2x² – 9x+7=0

3. x² – (√2+1) x + √2 =0