QUADRATIC EQUATIONS IN ONE VARIABLE
WBBSE MATH SOLUTION | GANIT PRAKASH SOLVE CLASS 10
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- CONSTRUCTION: TANGENT TO A CIRCLE – CLICK HERE
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- APPLICATION OF TRIGONOMETRIC RATIOS: HEIGHT AND DISTANCES – CLICK HERE
- STATISTICS: MEAN, MEDIAN, OGIVE, AND MODE – CLICK HERE
West Bengal Math book Ganit Prakash Class 10 solution you can get here. This will guide you to get the full solution of the chapter Quadratic Equations in one variable. You can get a solutions video lecture and many other things related to the chapter here.
Exercise Links
Let Us Work Out 1.1
Ganit Prakash Chapter 1 Exercise 1.1 Q No 1
1. write the quadratic polynomials from the following polynomials by understanding it.
(i) x2– 7x + 2
(ii) 7x5 – x(x + 2)
(iii) 2x (x+5) + 1
(iv) 2x – 1
Ganit Prakash Chapter 1 Exercise 1.1 Q No 2
2. Which of the following equations can be written in the form of ax2+ bx + c = 0, where a, b, c are real numbers and a ≠ 0, let us write it.
(i) x – 1 + 1/x = 6
(ii) x + 3/x = x2
(iii) x2 – 6 √ x +2 = 0
(iv) (x – 2)2= x2 – 4x + 4
Ganit Prakash Chapter 1 Exercise 1.1 Q No 3
3. Let us determine the power of the variable for which the equation x6 – x3 – 2 = 0 will become a quadratic equation?
Ganit Prakash Chapter 1 Exercise 1.1 Q No 4(i)
4 (i) Let us determine the value of ‘a’ for which the equation (a-2) x2+ 3x + 5=0 will not be a quadratic equation.
Ganit Prakash Chapter 1 Exercise 1.1 Q No 4(ii)
4 (ii) If be expressed in the form of ax2 + bx + c = 0 (a ≠ 0), then let us determine the co-efficient of x.
Ganit Prakash Chapter 1 Exercise 1.1 Q No 4(iii)
4 (iii) Let us express the equation 3x2 + 7x +23 = (x+4)(x+3) +2 in the form of the quadratic equation ax2 +bx + c = 0 (a # 0).
Ganit Prakash Chapter 1 Exercise 1.1 Q No 4(iv)
4 (iv) Let us express the equation (x+2)3 = x (x2 – 1) in the form of ax2 +bx + c = 0 (a # 0) and write the coefficient of x2,x and x0.
Ganit Prakash Chapter 1 Exercise 1.1 Q No 5(i)
5. Let us construct the quadratic equations in one variable from the following statements.
(i) Divide 42 into two parts such that one part is equal to the square of the other part.
Ganit Prakash Chapter 1 Exercise 1.1 Q No 5(ii)
(ii) The product of two consecutive positive odd numbers is 143.
Ganit Prakash Chapter 1 Exercise 1.1 Q No 5(iii)
(iii) The sum of the squares of two consecutive numbers is 313.
Ganit Prakash Chapter 1 Exercise 1.1 Q No 6(i)
6 (i). Let us construct the quadratic equations in one variable from the following statements.
The length of the diagonal of a rectangular area is 15 m. and the length exceeds its breadth by 3 m.
Ganit Prakash Chapter 1 Exercise 1.1 Q No 6(ii)
6(ii). Let us construct the quadratic equations in one variable from the following statements.
One person bought some kg. sugar in ₹ 80. If he would get 4 kg. more sugar with that money, then the price of kg. sugar would be less by ₹ 1.
Ganit Prakash Chapter 1 Exercise 1.1 Q No 6(iii)
6 (iii). Let us construct the quadratic equations in one variable from the following statements.
The distance between the two stations is 300 km. A train went to the second station from the first station with uniform velocity. If the velocity of the train is 5 km/hour more, then the time taken by the train to reach the second station would be lesser than 2 hours.
Ganit Prakash Chapter 1 Exercise 1.1 Q No 6(iv)
6 (iv). Let us construct the quadratic equations in one variable from the following statements.
A clock seller sold a clock by purchasing it at ₹ 336. The amount of his profit percentage is as much as the amount with which he bought the clock.
Ganit Prakash Chapter 1 Exercise 1.1 Q No 6(vi)
6 (vi) Let us construct the quadratic equations in one variable from the following statements.
The time taken to clean out the garden of Majid is 3 hours more than Mahim. Both of them together can complete the work in 2 hours.
Ganit Prakash Chapter 1 Exercise 1.1 Q No 6(vii)
6 (vii) Let us construct the quadratic equations in one variable from the following statements.
The unit digit of a two-digit number exceeds its tens’ digit by 6 and the product of two digits is less by 12 from the number.
Ganit Prakash Chapter 1 Exercise 1.1 Q No 6(viii)
6.(viii) Let us construct the quadratic equations in one variable from the following statements.
There is a road of equal width around the outside of a rectangular playground having the length 45 m. and breadth 40 m. and the area of the road is 450 sqm.
Let Us Work Out 1.2
Now lets solve the exercise
Ganit Prakash Chapter 1 Exercise 1.2 Q No 4(i)
4(i) 3y2-20 = 160 -2y2
Ganit Prakash Chapter 1 Exercise 1.2 Q No 4(ii)
4(ii) (2x+1)2 + (x+1)2=6x+47
Ganit Prakash Chapter 1 Exercise 1.2 Q No 4(iii)
4(iii) (x-7) (x-9) = 195
Ganit Prakash Chapter 1 Exercise 1.2 Q No 4(iv)
4 (iv) Let us solve : 3x- 24/x = x/3; x not equal to 0.
Ganit Prakash Chapter 1 Exercise 1.2 Q No 4(v)
4 (v) Let us solve : x/3 +3/x = 15/x, x is not equals to 0.
Let Us Work Out 1.3
WB Madhyamik Ganit Prakash for class 10 chapter 1 Quadratic Equation Exercise 1.3 is solved here. This whole book is solved.
Ganit Prakash Ch 1 Ex 1.3 Q No 1
The difference of two positive whole numbers is 3 and the sum of their squares is 117; by calculating, let us write the two numbers.
Ganit Prakash Ch 1 Ex 1.3 Q No 2
The base of a triangle is 18m. more than two times of its heights, if the area of the triangle is 360 sq.m., then let us determine the height of it.
Ganit Prakash Ch 1 Ex 1.3 Q No 3
If 5 times of a positive whole number is less by 3 than twice of its square, then let us determine the number.
Ganit Prakash Ch 1 Ex 1.3 Q No 4
The distance between two places is 200 km.; the time taken by 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.
Ganit Prakash Ch 1 Ex 1.3 Q No 5
The area of the Amita’s rectangular land is 2000 sq.m. and perimeter of it is 180 m. By calculating, let us write the length and breadth of the Amita’s land.
Ganit Prakash Ch 1 Ex 1.3 Q No 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.
Ganit Prakash Ch 1 Ex 1.3 Q No 7
There are two pipes in the water reservoir of our school. Two pipes together take 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.
Ganit Prakash Ch 1 Ex 1.3 Q No 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 Pijaush. Let us write, by calculating, the time taken by Porna alone to complete the work.
Ganit Prakash Ch 1 Ex 1.3 Q No 9
If the price of 1 dozen pens is reduced by ₹ 6, then 3 more pens will be got in ₹ 30. Before the reduction of price, let us calculate the price of 1 donzen pen.
Ganit Prakash Ch 1 Ex 1.3 Q No 10 A MCQ TYPE
(i) The number of roots of a quadratic equation is
A. one
B. two
C. three
D. none of them
(ii) If in a ax2+ bx + c quadratic equation, then
A. b ≠ 0
B. C ≠ 0
C. a ≠ 0
D. none of these
(iii) The highest power of the variable in a quadratic equation is
A. 1
B. 2
C. 3
D. none of these.
(iv) The equation 4(5x2– 7x + 2)=5 (4x2 – 6x + 3) is
A. linear
B. quadratic
C. 3rd degree
D. none of these
(v) The root/two roots of the equation.
A. 0
B. 6
C. 0 & 6
D. -6
Ganit Prakash Ch 1 Ex 1.3 Q No 10 B TRUE/FALSE TYPE
i. (x-3)2 = x2 – 6x + 9 is a quadratic equation
ii. 5 is the only one root of the equation x2 = 25
Ganit Prakash Ch 1 Ex 1.3 Q No 10 C FILL IN THE BLANKS TYPE
- If a = 0 and b ≠ 0 in the equation ax2+ bx + c = 0, then the equation is a …………………. equation.
- The two roots of the equation x2= 6x are ……………. & ………………
Ganit Prakash Ch 1 Ex 1.3 Q No 11 C SA Q No 1
Let us find the value of a if one root of the equation x2+ax+3=0 is 1
Ganit Prakash Ch 1 Ex 1.3 Q No 11 C SA Q No 2
Let us write the value of the other root if one root of the equation x2– (2 + b) x + 6 = 0 is 2.
Ganit Prakash Ch 1 Ex 1.3 Q No 11 C SA Q No 3
Let us write the value of the other root if one root of the equation 2x2+ kx + 4 = 0 is 2.
Let Us Work Out 1.4
Ganit Prakash Class 10 Chapter 1 Quadratic Equation in one variable Exercise 1.4 is solved in this video lecture.
Ganit Prakash Ch 1 Ex 1.4 Q No 1(i)
Let us write whether Sridhara Acharyya’s formula is applicable or not applicable to solve the equation 4×2+(2x-1) (2x+1)=4x(2x-1)
Ganit Prakash Ch 1 Ex 1.4 Q No 1(ii)
Let us write what type of equation can be solved with the help of Sridhara Acharyya’s formula.
Ganit Prakash Ch 1 Ex 1.4 Q No 1(iii)
By applying Sridhara Acharyya’s formula in the equation 5x²+2x-7=0, it is found that x=(k+-12)/10, let us write by calculating, what will be the value of k.
Ganit Prakash Ch 1 Ex 1.4 Q No 2(i)
If the following quadratic equations have real roots, then let us determine them with the help of Sridhara Acharyya’s formula.
(i) 3x²+11x-4=0
Ganit Prakash Ch 1 Ex 1.4 Q No 2(ii)
If the following quadratic equations have real roots, then let us determine them with the help of Sridhara Acharyya’s formula.
(ii) (x-2)(x+4)+9=0
Ganit Prakash Ch 1 Ex 1.4 Q No 2(iii)
If the following quadratic equations have real roots, then let us determine them with the help of Sridhara Acharyya’s formula.
(iii) (4x-3)²-2(x+3)=0
Ganit Prakash Ch 1 Ex 1.4 Q No 2(iv)
If the following quadratic equations have real roots, then let us determine them with the help of Sridhara Acharyya’s formula.
(iv) 3x²+2x-1=0
Ganit Prakash Ch 1 Ex 1.4 Q No 2(v)
If the following quadratic equations have real roots, then let us determine them with the help of Sridhara Acharyya’s formula.
(v) 3x²+2x+1=0
Ganit Prakash Ch 1 Ex 1.4 Q No 2(vi)
If the following quadratic equations have real roots, then let us determine them with the help of Sridhara Acharyya’s formula.
(vi) 10x²-x-3=0
Ganit Prakash Ch 1 Ex 1.4 Q No 2(vii)
If the following quadratic equations have real roots, then let us determine them with the help of Sridhara Acharyya’s formula.
(vii) 10x²-x+3=0
Ganit Prakash Ch 1 Ex 1.4 Q No 2(viii)
If the following quadratic equations have real roots, then let us determine them with the help of Sridhara Acharyya’s formula.
(viii) 25x²-30x+7=0
Ganit Prakash Ch 1 Ex 1.4 Q No 2(ix)
If the following quadratic equations have real roots, then let us determine them with the help of Sridhara Acharyya’s formula.
(ix) (4x-2)²+6x=25
Ganit Prakash Ch 1 Ex 1.4 Q No 3(i)
Sathi has drawn a right-angled triangle whose length of the hypotenuse is 6cm. more than the 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 three sides of the right-angled triangle drawn by Sathi.
Ganit Prakash Ch 1 Ex 1.4 Q No 3(ii)
If a two digit positive number is multiplied by its unit digit, then the product is 189 and if the tens digit is twice of the unit digit, then let us calculate the unit digit.
Ganit Prakash Ch 1 Ex 1.4 Q No 3(iii)
The speed of Salma is 1m/second more than the speed of Anik. In a 180 m race, Salma reaches 2 seconds before than Anik. Let us write by calculating the speed of Anik in m/sec.
Ganit Prakash Ch 1 Ex 1.4 Q No 3(iv)
There is a square park in our locality. The area of a rectangular park is 78 sqm. less than the twice of the area of that square-shaped park whose length is 5m. more than the length of the side of that park and the breadth is 3m. 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.
Ganit Prakash Ch 1 Ex 1.4 Q No 3(v)
In our village, Proloy babu bought 350 chilli plants for planting in his rectangular land. when he put the plants in rows, he noticed that, if he would put 24 plants more than the number of rows in each row, 10 plants would remain excess. Let us write by calculating the number of rows.
Ganit Prakash Ch 1 Ex 1.4 Q No 3(vi)
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.
Ganit Prakash Ch 1 Ex 1.4 Q No 3(vii)
The speed of a boat in still water is 8 kms/hr. If the boat can go 15 kms. down stream and 22 kms. up stream in 5 hours, then let us write by calculating, the speed of the stream.
Ganit Prakash Ch 1 Ex 1.4 Q No 3(viii)
A superfast train runs at the speed of 15 kms/hr more than that of an express train. Leaving the same station the superfast train reached a station of 180 kms. distance 1hour before than the express train. Let us determine the speed of the superfast train in km/hr.
Ganit Prakash Ch 1 Ex 1.4 Q No 3(ix)
Rehana went to the market and saw that the price of dal of 1kg. is 20 and the price of rice of 1 kg. is 40 less than that of price of 1 kg fish. The total quantity of fish and that of dal each in 240 is equal to the quantity of rice in 280. Let us calculate the cost price of 1 kg. fish.
Let Us Work Out 1.5
Ganit Prakash Class 10 Chapter 1 Quadratic Equation in one variable Exercise 1.5 is solved in this video lecture.
Ganit Prakash Ch 1 Ex 1.5 Q No 1
Let us write the nature of two roots of the following quadratic equations:
(i) 2x²+7x+3=0
(ii) 3x²-2√6x+2=0
(iii) 2x²-7x+9=0
(iv) 2/5x²-2/3x+1=0
Ganit Prakash Ch 1 Ex 1.5 Q No 2
By calculating, let us write the value/values of k for which each of the following quadratic equations has real and equal roots-
(i) 49x²+kx+1=0
(ii) 3x²–5x+2k-0
(iii) 9x²-24x+k=0
(iv) 2x²+3x+k=0
(v) x²-2(5+2k)x+3(7+10k)=0
(vi) (3k+1)x²+2(k+1)x+k=0
Ganit Prakash Ch 1 Ex 1.5 Q No 3
Let us form the quadratic equations from two roots given below-
(i) 4,2 (ii)-4,-3 (iii)-4,3 (iv) 5,-3
Ganit Prakash Ch 1 Ex 1.5 Q No 4
What value of m for which two roots of the quadratic equation 4x²+4(3m-1)x+(m+7)=0 are reciprocal to each other.
Ganit Prakash Ch 1 Ex 1.5 Q No 5
If two roots of the quadratic equation (b-c)x²+(c-a)x+(a-b)=0 are equal, then let us prove that, 2b=a+c.
Ganit Prakash Ch 1 Ex 1.5 Q No 6
If two roots of the quadratic equation (a²+b²)x²-2(ac+bd)x+(c²+d²)=0 are equal, then let us prove that, a/b=c/d.
Ganit Prakash Ch 1 Ex 1.5 Q No 7
Let us prove that, the quadratic equation 2(a²+b²)x²+2(a+b)x+1=0 has no real root, if a=/b.
Ganit Prakash Ch 1 Ex 1.5 Q No 8
If two roots of the quadratic equation 5x²+2x-3-0 are a and b, then let us determine the value of,
(i) a²+b²
(ii) a³+b³
(iii) 1/a+1/b
(iv) a²/b +b²/a
Ganit Prakash Ch 1 Ex 1.5 Q No 9
If one root of the equation ax²+bx+c=0 is twice of the other, then let us show that, 2b²=9ac.
Ganit Prakash Ch 1 Ex 1.5 Q No 10
Let us form the equation whose roots are reciprocals to the roots of the equation x²+px+1=0.
Ganit Prakash Ch 1 Ex 1.5 Q No 11
Let us determine the equation whose roots are square of the roots of the equation x²+x+1=0.
Ganit Prakash Ch 1 Ex 1.5 Q No 12A MCQ
(A) M.C.Q.:
(i) The sum of two roots of the equation x²-6x+2=0 is
(a) 2 (b)-2 (c) 6 (d)-6
(ii) If the product of two roots of the equation x2-3x+k-10 is-2, then the value of k is
(a)-2 (b)-8 (c) 8 (d) 12
(iii) If two roots of the equation ax²+bx+c=0 (ax0) are real and unequal, then b²-4ac will be
(a) >0 (b)=0 (c) <0 (d) none of these
(iv) If two roots of the equation ax²+bx+c=0 (a=/0) be equal, then
(a) c= – b/2a (b) c = b/2a (c) c = -b²/4a (d) c = b²/4a
(v) If two roots of the equation 3x²+8x+2=0 be a and b, then the value of (1/a+1/b) is
(a)-3/8 (b) 2/3 (c)-4 (d) 4
Ganit Prakash Ch 1 Ex 1.5 Q No 12 B TRUE/FALSE TYPE
Let us write whether the following statements are true or false :
(i) The two roots of the equation x²+x+1=0 are real.
(ii) The two roots of the equation x²-x+2=0 are not real.
Ganit Prakash Ch 1 Ex 1.5 Q No 12 C FILL IN THE BLANKS TYPE
Let us fill in the blanks :
(i) The ratio of the sum and the product of two roots of the equation 7×2²-12x+18=0 is ____.
(ii) If two roots of the equation ax²+bx+c=0 (a #0) are reciprocal to each other, then C= ___ .
(iii) If two roots of the equation ax²+bx+c=0 (a#0) are reciprocal to each other and opposite in sign, then a+c=.____.
Ganit Prakash Ch 1 Ex 1.5 Q No 13 (i)
Let us write the quadratic equation if sum of its roots is 14 and the product of them is 24.
Ganit Prakash Ch 1 Ex 1.5 Q No 13 (ii)
If the sum and the product of two roots of the equation kx²+2x+3k=0 (k = 0) are equal, let us write the value of k.
Ganit Prakash Ch 1 Ex 1.5 Q No 13 (iii)
If two roots of the equation x²-22x+105=0 are a and b, let us write the value of (a-b).
Ganit Prakash Ch 1 Ex 1.5 Q No 13 (iv)
If the sum of two roots of the equation x²-x=k (2x-1) is zero, let us write the value Of k.
Ganit Prakash Ch 1 Ex 1.5 Q No 13 (v)
If one of the roots of the two equations x²+bx+12=0 and x²+bx+q=0 is 2, let us write the value of q.