WBBSE Solutions For Class 10 Maths Chapter 1 Quadratic Equations In One Variable Exercise 1.4

Chapter 1 Quadratic Equations In One Variable Exercise 1.4

Wbbse Class 10 Quadratic Equation Formula Question 1.

Let us write by understanding whether Sreedhar Acharya’s formula is applicable or not applicable to solve the equation 4×2 + (2x-1) (2x + 1) = 4x (2x-1).

Solution: 4x² + (2x-1) (2x + 1) = 4x (2x-1)

=> 4x² + 4x² – 1 = 8x² – 4x

=> 8x²-8x²+4x-1=0

=> 4x-1=0

It is a linear equation of one variable. So, it is not possible to apply Sreedhar Acharya’s formula.

Read and Learn More WBBSE Solutions For Class 10 Maths

Question 2.

Let us write by understanding what type of equation can be solved with the help of Sreedhar Acharyya’s formula.

Solution: Quadratic equation in one variable.

Wbbse Class 10 Quadratic Equation Formula   Question 3.

By applying Sreedhar Acharyya’s formula in equation 5×2 + 2x-7= 0, it is found that x = k±12/10; let us write by calculating what will be the value of k.

If the following quadratic equations have real roots, then let us determine them with the help of Sreedhar Acharyya’s formula.

1. 3x²+11x-4=0

2. (x-2) (x+4) +9=0

3. (4x-3)²-2(x+3) = 0

4. 3x² + 2x-1=0

5. 3x² + 2x+1=0

6. 10x²-x-3=0

7. 10x²-x+3=0

8. 25x²-30x+7=0

9. (4x-2)²+6x= 25

Wbbse Class 10 Maths Chapter 1 Exercise 1.4 Solutions

Question 3. Let us express the following mathematical problems in the form of quadratic equations with one variable and solve them by applying Sreedhar Acharyya’s formula or with the help of factorization.

1. Sathi has drawn a right-angled triangle whose length of the hypotenuse is 6 cm more than twice of the shortest side. If the length of the third side is 2 cm less than the length of the hypotenuse, then by calculating, let us write the lengths of the three sides of the right-angled triangle drawn by Sathi.

2. If a two-digit positive number is multiplied by its unit digit, then the product is 189 and if the ten’s digit is twice of the unit digit, then let us calculate the unit digit.

3. The speed of Salma is 1m/second more than the speed of Anik. In a 180 m run, Salma reaches 2 seconds before Anik. Let us write by calculating the speed of Anik in m/sec.

4. There is a square park in our locality. The area of a rectangular park is 78 sqm less than the twice of area of that square-shaped park whose length is 5 m more than the length of the side of that park and the breadth is 3 m less than the length of the side of that park. Let us write by calculating the length of the side of the square- shaped park.

⇒ (x-9)(x+7)=0

∴ Eitherx-9=0       ∴x=9.

Or, x+7=0            ∴x=-7 (Not possible)

∴ Length of each side of the square field=9 m. Ans.

5. In our village, Proloy babu bought 350 chili plants for planting on his rectangular land. When he put the plants in rows, he noticed that if he would put 24 rows more than the number of plants in each row, 10 plants would remain in excess. Let us write by calculating the number of plants he put in each row.

Wbbse Class 10 Maths Chapter 1 Exercise 1.4 Solutions

6. Joseph and Kuntal work in a factory. Joseph takes 5 minutes less time than Kuntal to make a product. Joseph makes 6 products more than Kuntal while working for 6 hours. Let us write by calculating, the number of products Kuntal makes during that time.

Wbbse Class 10 Maths Chapter 1 Exercise 1.4 Solutions

7. The speed of a boat in still water is 8 km/hr. If the boat can go 15 km downstream and 22 km upstream in 5 hours, then let us write by calculating, the speed of the stream.

Wbbse Class 10 Maths Chapter 1 Exercise 1.4 Solutions

8. A superfast train runs having a speed of 15 km/hr more than that of an express train. Leaving the same station the superfast train reached a station of 180 km distance 1 hour before that the express train. Let us determine the speed of the superfast train in km/hr.

9. Rehana went to the market and saw that the price of dal of 1 kg is Rs. 20 and the price of rice of 1 kg Is Rs. 40 less than that of fish of 1 kg. The quantity of fish and that of dal in Rs. 240 is equal to the quantity of rice in Rs. 280. Let us calculate the cost price of 1 kg of fish.

Application 1. I determine the nature of the two roots of the following quadratic equations: 2x²+x-2

Application 2. By understanding, let us write the value of k for which the two roots of the quadratic equation 2x² – 10x + k = 0 are real and equal. 

Application 3. I determine the sum and product of two roots of the quadratic equations: 4x²-9x=100

Solution: 4x²-9x-100 = 0

 

Application 4. If one of the roots of the quadratic equation 3x² – 10x + 3 = 0 is then let me 3′. determine the other root of it. 

Application 5. If a and ẞ are two roots of the quadratic equation ax² + bx + c = 0 [a + 0], then let Us express the value of (1/α² + 1/ ẞ²) in terms of a, b, and c.

Application 6. By determining, we are observing that two roots of the quadratic equation x²-7x+12= 0 are 3 and 4.