Algebra · Textbook solutions

Quadratic Equations

Every solved example, exercise, and miscellaneous question, in the order the textbook teaches them. Plus every board question asked from this chapter. · 135 questions

Standard form of quadratic equation

4 q

Solved Examples

Worked · 4

Decide which of the following are quadratic equations ?
Standard form of quadratic equation SolvedEx.1 (1) $3x^2 - 5x + 3 = 0$
Standard form of quadratic equation SolvedEx.1 (2) $9y^2 + 5 = 0$
Standard form of quadratic equation SolvedEx.1 (3) $m^3 - 5m^2 + 4 = 0$
Standard form of quadratic equation SolvedEx.1 (4) $(l + 2)(l - 5) = 0$

Roots of a quadratic equation

1 q

Solved Example

Worked · 1

Roots of a quadratic equation SolvedEx.1 $2x^2 - 7x + 6 = 0$

Practice Set 2.1

17 q

Ex 2.1 Q.1 $Write any two quadratic equations.$
Decide which of the following are quadratic equations.
Ex 2.1 Q.2 (1) $x^2 + 5x - 2 = 0$
Ex 2.1 Q.2 (2) $y^2 = 5y - 10$
Ex 2.1 Q.2 (3) $y^2 + \dfrac{1}{y} = 2$
Ex 2.1 Q.2 (4) $x + \dfrac{1}{x} = -2$
Ex 2.1 Q.2 (5) $(m + 2)(m - 5) = 0$
Ex 2.1 Q.2 (6) $m^3 + 3m^2 - 2 = 3m^3$
Write the following equations in the form $ax^2 + bx + c = 0$ , then write the values of $a, b, c$ for each equation.
Ex 2.1 Q.3 (1) $2y = 10 - y^2$
Ex 2.1 Q.3 (2) $(x - 1)^2 = 2x + 3$
Ex 2.1 Q.3 (3) $x^2 + 5x = -(3 - x)$
Ex 2.1 Q.3 (4) $3m^2 = 2m^2 - 9$
Ex 2.1 Q.3 (5) $P(3 + 6p) = -5$
Ex 2.1 Q.3 (6) $x^2 - 9 = 13$
Determine whether the values given against each of the quadratic equation are the roots of the equation.
Ex 2.1 Q.4 (1) $x^2 + 4x - 5 = 0$
Ex 2.1 Q.4 (2) $2m^2 - 5m = 0$
Ex 2.1 Q.5 $k$
Ex 2.1 Q.6 $5m^2 + 2m + k = 0$

Solutions of a quadratic equation by factorisation

5 q

Solved Examples

Worked · 5

Solve the following quadratic equations by factorisation.
Solutions of a quadratic equation by factorisation SolvedEx.1 (1) $m^2 - 14m + 13 = 0$
Solutions of a quadratic equation by factorisation SolvedEx.1 (2) $3x^2 - x - 10 = 0$
Solutions of a quadratic equation by factorisation SolvedEx.1 (3) $3y^2 = 15y$
Solutions of a quadratic equation by factorisation SolvedEx.1 (4) $x^2 = 3$
Solutions of a quadratic equation by factorisation SolvedEx.1 (5) $6\sqrt{3}\,x^2 + 7x = \sqrt{3}$

Practice Set 2.2

12 q

Solve the following quadratic equations by factorisation.
Ex 2.2 Q.1 (1) $x^2 - 15x + 54 = 0$
Ex 2.2 Q.1 (2) $x^2 + x - 20 = 0$
Ex 2.2 Q.1 (3) $2y^2 + 27y + 13 = 0$
Ex 2.2 Q.1 (4) $5m^2 = 22m + 15$
Ex 2.2 Q.1 (5) $2x^2 - 2x + \dfrac{1}{2} = 0$
Ex 2.2 Q.1 (6) $6x - \dfrac{2}{x} = 1$
Ex 2.2 Q.1 (7) $\sqrt{2}\,x^2 + 7x + 5\sqrt{2} = 0$
Ex 2.2 Q.1 (8) $3x^2 - 2\sqrt{6}\,x + 2 = 0$
Ex 2.2 Q.1 (9) $2m(m - 24) = 50$
Ex 2.2 Q.1 (10) $25m^2 = 9$
Ex 2.2 Q.1 (11) $7m^2 = 21m$
Ex 2.2 Q.1 (12) $m^2 - 11 = 0$

Solution of a quadratic equation by completing the square

2 q

Solved Examples

Worked · 2

Solution of a quadratic equation by completing the square SolvedEx.1 $5x^2 - 4x - 3 = 0$
Solution of a quadratic equation by completing the square SolvedEx.2 $x^2 + 8x - 48 = 0$

Practice Set 2.3

6 q

Solve the following quadratic equations by completing the square method.
Ex 2.3 (1) $x^2 + x - 20 = 0$
Ex 2.3 (2) $x^2 + 2x - 5 = 0$
Ex 2.3 (3) $m^2 - 5m = -3$
Ex 2.3 (4) $9y^2 - 12y + 2 = 0$
Ex 2.3 (5) $2y^2 + 9y + 10 = 0$
Ex 2.3 (6) $5x^2 = 4x + 7$

Formula for solving a quadratic equation

5 q

Solved Examples

Worked · 5

Solve quadratic equations using formula.
Formula for solving a quadratic equation SolvedEx.1 $m^2 - 14m + 13 = 0$
Formula for solving a quadratic equation SolvedEx.2 $x^2 + 10x + 2 = 0$
Formula for solving a quadratic equation SolvedEx.3 $x^2 - 2x - 3 = 0$
Formula for solving a quadratic equation SolvedEx.4 $25x^2 + 30x + 9 = 0$
Formula for solving a quadratic equation SolvedEx.5 $x^2 + x + 5 = 0$

Practice Set 2.4

10 q

Compare the given quadratic equations to the general form and write values of $a, b, c$ .
Ex 2.4 Q.1 (1) $x^2 - 7x + 5 = 0$
Ex 2.4 Q.1 (2) $2m^2 = 5m - 5$
Ex 2.4 Q.1 (3) $y^2 = 7y$
Solve using formula.
Ex 2.4 Q.2 (1) $x^2 + 6x + 5 = 0$
Ex 2.4 Q.2 (2) $x^2 - 3x - 2 = 0$
Ex 2.4 Q.2 (3) $3m^2 + 2m - 7 = 0$
Ex 2.4 Q.2 (4) $5m^2 - 4m - 2 = 0$
Ex 2.4 Q.2 (5) $y^2 + \dfrac{1}{3}y = 2$
Ex 2.4 Q.2 (6) $5x^2 + 13x + 8 = 0$
Ex 2.4 Q.3 $x^2 + 2\sqrt{3}\,x + 3 = 0$

Nature of roots of a quadratic equation

4 q

Solved examples

Worked · 4

Nature of roots of a quadratic equation SolvedEx.1 $x^2 + 10x - 7 = 0$
Determine nature of roots of the quadratic equations.
Nature of roots of a quadratic equation SolvedEx.2 (i) $2x^2 - 5x + 7 = 0$
Nature of roots of a quadratic equation SolvedEx.2 (ii) $x^2 + 2x - 9 = 0$
Nature of roots of a quadratic equation SolvedEx.3 $\sqrt{3}\,x^2 + 2\sqrt{3}\,x + \sqrt{3} = 0$

The relation between roots of the quadratic equation and coefficients

3 q

Solved examples

Worked · 3

The relation between roots of the quadratic equation and coefficients SolvedEx.1 $\alpha$
The relation between roots of the quadratic equation and coefficients SolvedEx.2 $x^2 - 13x + k = 0$
The relation between roots of the quadratic equation and coefficients SolvedEx.3 $\alpha$

To obtain a quadratic equation having given roots

1 q

Solved examples

Worked · 1

To obtain a quadratic equation having given roots SolvedEx.1 $-3, -7$

Practice Set 2.5

18 q

Activity : Fill in the gaps and complete.
Ex 2.5 Q.1 (1) $ax^2 + bx + c = 0$
Ex 2.5 Q.1 (2) $= -7$
Ex 2.5 Q.1 (3) $\alpha$
Find the value of discriminant.
Ex 2.5 Q.2 (1) $x^2 + 7x - 1 = 0$
Ex 2.5 Q.2 (2) $2y^2 - 5y + 10 = 0$
Ex 2.5 Q.2 (3) $\sqrt{2}\,x^2 + 4x + 2\sqrt{2} = 0$
Determine the nature of roots of the following quadratic equations.
Ex 2.5 Q.3 (1) $x^2 - 4x + 4 = 0$
Ex 2.5 Q.3 (2) $2y^2 - 7y + 2 = 0$
Ex 2.5 Q.3 (3) $m^2 + 2m + 9 = 0$
Form the quadratic equation from the roots given below.
Ex 2.5 Q.4 (1) $0 and 4$
Ex 2.5 Q.4 (2) $-10$
Ex 2.5 Q.4 (3) $\dfrac{1}{2}, -\dfrac{1}{2}$
Ex 2.5 Q.4 (4) $2 - \sqrt{5}, \ 2 + \sqrt{5}$
Ex 2.5 Q.5 $k$
$\alpha$ , $\beta$ are roots of $y^2 - 2y - 7 = 0$ find,
Ex 2.5 Q.6 (1) $\alpha^2 + \beta^2$
Ex 2.5 Q.6 (2) $\alpha^3 + \beta^3$
The roots of each of the following quadratic equations are real and equal, find $k$ .
Ex 2.5 Q.7 (1) $3y^2 + ky + 12 = 0$
Ex 2.5 Q.7 (2) $kx(x - 2) + 6 = 0$

Application of quadratic equation

2 q

Solved examples

Worked · 2

Application of quadratic equation SolvedEx.1 $There is a rectangular onion storehouse in the farm of Mr. Ratnakarrao at Tivasa. The length of rectangular base is more than its breadth by 7 m and diagonal is more than length by 1 m. Find length and breadth of the storehouse.$
Application of quadratic equation SolvedEx.2 $A train travels 360 km with uniform speed. The speed of the train is increased by 5 km/hr, it takes 48 minutes less to cover the same distance. Find the initial speed of the train.$

Practice Set 2.6

10 q

Ex 2.6 Q.1 $Product of Pragati's age 2 years ago and 3 years hence is 84. Find her present age.$
Ex 2.6 Q.2 $Sum of squares of 2 consecutive natural even numbers is 244; find the numbers.$
Ex 2.6 Q.3 $x$
Ex 2.6 Q.4 $\dfrac{1}{6}$
Ex 2.6 Q.5 $Suyash scored 10 marks more in second test than that in the first. 5 times the score of the second test is the same as square of the score in the first test. Find his score in the first test.$
Ex 2.6 Q.6 $Mr. Kasam runs a small business of making earthen pots. He makes certain number of pots on daily basis. Production cost of each pot is ₹ 40 more than 10 times total number of pots, he makes in one day. If production cost of all pots per day is ₹ 600, find production cost of one pot and number of pots he makes per day.$
Ex 2.6 Q.7 $Pratik takes 8 hours to travel 36 km downstream and return to the same spot. The speed of boat in still water is 12 km. per hour. Find the speed of water current.$
Ex 2.6 Q.8 $Pintu takes 6 days more than those of Nishu to complete certain work. If they work together they finish it in 4 days. How many days would it take to complete the work if they work alone.$
Ex 2.6 Q.9 $If 460 is divided by a natural number, quotient is 6 more than five times the divisor and remainder is 1. Find quotient and diviser.$
Ex 2.6 Q.10 $\square ABCD$

Problem Set 2

35 q

Choose the correct answers for the following questions.
PS2 Q.1 (1) $Which one is the quadratic equation ?$
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PS2 Q.1 (2) $Out of the following equations which one is not a quadratic equation ?$
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PS2 Q.1 (3) $x^2 + kx + k = 0$
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PS2 Q.1 (4) $\sqrt{2}\,x^2 - 5x + \sqrt{2} = 0$
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PS2 Q.1 (5) $Which of the following quadratic equations has roots 3, 5 ?$
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PS2 Q.1 (6) $-5$
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PS2 Q.1 (7) $\sqrt{5}\,m^2 - \sqrt{5}\,m + \sqrt{5} = 0$
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PS2 Q.1 (8) $x^2 + mx - 5 = 0$
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Which of the following equations is quadratic ?
PS2 Q.2 (1) $x^2 + 2x + 11 = 0$
PS2 Q.2 (2) $x^2 - 2x + 5 = x^2$
PS2 Q.2 (3) $(x + 2)^2 = 2x^2$
Find the value of discriminant for each of the following equations.
PS2 Q.3 (1) $2y^2 - y + 2 = 0$
PS2 Q.3 (2) $5m^2 - m = 0$
PS2 Q.3 (3) $\sqrt{5}\,x^2 - x - \sqrt{5} = 0$
PS2 Q.4 $2x^2 + kx - 2 = 0$
Two roots of quadratic equations are given ; frame the equation.
PS2 Q.5 (1) $-10$
PS2 Q.5 (2) $1 - 3\sqrt{5}$
PS2 Q.5 (3) $0 and 7$
Determine the nature of roots for each of the quadratic equation.
PS2 Q.6 (1) $3x^2 - 5x + 7 = 0$
PS2 Q.6 (2) $\sqrt{3}\,x^2 + \sqrt{2}\,x - 2\sqrt{3} = 0$
PS2 Q.6 (3) $m^2 - 2m + 1 = 0$
Solve the following quadratic equations.
PS2 Q.7 (1) $\dfrac{1}{x + 5} = \dfrac{1}{x^2}$
PS2 Q.7 (2) $x^2 - \dfrac{3x}{10} - \dfrac{1}{10} = 0$
PS2 Q.7 (3) $(2x + 3)^2 = 25$
PS2 Q.7 (4) $m^2 + 5m + 5 = 0$
PS2 Q.7 (5) $5m^2 + 2m + 1 = 0$
PS2 Q.7 (6) $x^2 - 4x - 3 = 0$
PS2 Q.8 $m$
PS2 Q.9 $The sum of two roots of a quadratic equation is 5 and sum of their cubes is 35, find the equation.$
PS2 Q.10 $2x^2 + 2(p + q)x + p^2 + q^2 = 0$
PS2 Q.11 $Mukund possesses ₹ 50 more than what Sagar possesses. The product of the amount they have is 15,000. Find the amount each one has.$
PS2 Q.12 $The difference between squares of two numbers is 120. The square of smaller number is twice the greater number. Find the numbers.$
PS2 Q.13 $Ranjana wants to distribute 540 oranges among some students. If 30 students were more each would get 3 oranges less. Find the number of students.$
PS2 Q.14 $\dfrac{1}{3}$
PS2 Q.15 $A tank fills completely in 2 hours if both the taps are open. If only one of the taps is open at the given time, the smaller tap takes 3 hours more than the larger one to fill the tank. How much time does each tap take to fill the tank completely ?$

What the board has asked from this chapter

Questions per paper · 13 papers · 2016 to 2026

June 2026

4 q

Q1(A)(ii) $x^2 + mx - 5 = 0$
Tap an option to check your answer.
Roots of a Quadratic Equation
Q2(B)(ii) $-10$
Relation between Roots and Coefficients
Q2(B)(iv) $25m^2 = 9$
Solving by Factorisation
Q3(B)(ii) $x^2 - 3x - 2 = 0$
Solving by Formula and Completing the Square

March 2026

5 q

Q1(A)(ii) $खालीलपैकी कोणते समीकरण वर्गसमीकरण नाही ? Out of the following equations which one is not a quadratic equation?$
Tap an option to check your answer.
Roots of a Quadratic Equation
Q1(B)(iv) $ax^2 + bx + c = 0$
Roots of a Quadratic Equation
Q2(B)(iii) $x^2 + x - 20 = 0$
Solving by Factorisation
Q3(A)(ii) $5m^2 + 2m + k = 0$
Roots of a Quadratic Equation
Q4(i) $एका वर्गसमीकरणाच्या दोन मुळांची बेरीज 7 आणि त्यांच्या घनांची बेरीज 91 आहे तर ते वर्गसमीकरण कोणते ? The sum of two roots of a quadratic equation is 7 and sum of their cubes is 91, find the equation.$
Relation between Roots and Coefficients

July 2025

5 q

Q1(B)(ii) $2y = 10 - y^2$
Roots of a Quadratic Equation
Q2(A)(i) $x^2 + 8x - 48 = 0$
Solving by Formula and Completing the Square
Q2(B)(ii) $x^2 - 15x + 54 = 0$
Solving by Factorisation
Q3(B)(iii) $श्रद्धाच्या 2 वर्षापूर्वीच्या आणि 3 वर्षानंतरच्या वयांचा गुणाकार 84 आहे, तर तिचे आजचे वय काढा. Product of Shraddha's age 2 years ago and 3 years hence is 84. Find her present age.$
Word Problems and Applications
Q5(i) $\Delta = 0$
Nature of Roots (Discriminant)

March 2025

5 q

Q1(A)(ii) $खालीलपैकी कोणते समीकरण वर्गसमीकरण आहे ? From the following equations which one is the quadratic equation?$
Tap an option to check your answer.
Roots of a Quadratic Equation
Q2(A)(ii) $5$
Relation between Roots and Coefficients
Q2(B)(ii) $m^2 + 14m + 13 = 0$
Solving by Factorisation
Q3(B)(ii) $x^2 - 2x - 3 = 0$
Solving by Formula and Completing the Square
Q4(i) $(m - 12)x^2 + 2(m - 12)x + 2 = 0$
Nature of Roots (Discriminant)

July 2024

5 q

Q1(A)(ii) $खालीलपैकी कोणते समीकरण हे वर्गसमीकरण आहे ? Which equation from the following is a quadratic equation?$
Tap an option to check your answer.
Roots of a Quadratic Equation
Q2(A)(ii) $m^2 + 2m + 9 = 0$
Nature of Roots (Discriminant)
Q2(B)(ii) $x = 3$
Roots of a Quadratic Equation
Q3(B)(ii) $y^2 + \dfrac{1}{3}y = 2$
Solving by Formula and Completing the Square
Q4(i) $मनीषाला वाढदिवसानिमित्त 540 केळी काही विद्यार्थ्यांना समान वाटायची आहेत. जर 30 विद्यार्थी जास्त असते तर प्रत्येकाला 3 केळी कमी मिळाली असती, तर विद्यार्थ्यांची संख्या काढा. Manisha wants to distribute 540 bananas among some students. If 30 students were more, each would get 3 bananas less. Find the number of students.$
Word Problems and Applications

March 2024

5 q

Q1(A)(i) $kx^2 - 7x + 12 = 0$
Tap an option to check your answer.
Roots of a Quadratic Equation
Q2(A)(ii) $जर 2 आणि 5 ही वर्गसमीकरणाची मुळे आहेत, तर वर्गसमीकरण तयार करण्यासाठी खालील कृती पूर्ण करा : If 2 and 5 are the roots of a quadratic equation, then complete the activity to form the quadratic equation.$
Relation between Roots and Coefficients
Q2(B)(ii) $x^2 + x - 20 = 0$
Solving by Factorisation
Q3(B)(i) $3m^2 - m - 10 = 0$
Solving by Formula and Completing the Square
Q4(i) $एक टाकी दोन नळाच्या साहाय्याने 6 तासात पूर्ण भरते. ती टाकी भरण्यास लहान नळाला मोठ्या नळापेक्षा 5 तास जास्त लागतात तर प्रत्येक नळाने ती टाकी भरण्यास किती वेळ लागेल ? A tank can be filled up by two taps in 6 hours. The smaller tap alone takes 5 hours more than the bigger tap alone. Find the time required by each tap to fill the tank separately.$
Word Problems and Applications

March 2023

5 q

Q1(A)(ii) $Out of the following equations which one is NOT a quadratic equation?$
Tap an option to check your answer.
Roots of a Quadratic Equation
Q2(A)(ii) $x^2 + 2x - 9 = 0$
Nature of Roots (Discriminant)
Q2(B)(ii) $ax^2 + bx + c = 0$
Roots of a Quadratic Equation
Q3(B)(ii) $x^2 + 10x + 2 = 0$
Solving by Formula and Completing the Square
Q4(iii) $पाच क्रमागत नैसर्गिक संख्यांच्या वर्गांची बेरीज 1455 तर त्या संख्या शोधा. The sum of the squares of five consecutive natural numbers is 1455. Find the numbers.$
Word Problems and Applications

March 2022

6 q

Four alternative answers are given for every subquestion. Choose the correct alternative and write its alphabet with subquestion number.
Q1(A)(i) $Which one is the quadratic equation?$
Tap an option to check your answer.
Roots of a Quadratic Equation
Solve the following subquestions:
Q1(B)(ii) $2$
Roots of a Quadratic Equation
Solve the following subquestions (any four):
Q2(B)(iv) $x^2 + x - 20 = 0$
Solving by Factorisation
Complete the following activity and rewrite it (any one):
Q3(A)(i) $kx^2 - 10x + 3 = 0$
Roots of a Quadratic Equation
Solve the following subquestions (any two):
Q3(B)(iv) $x^2 + 10x + 2 = 0$
Solving by Formula and Completing the Square
Solve the following subquestions (any two):
Q4(i) $If 460 is divided by a natural number, then the quotient is 2 more than nine times the divisor and the remainder is 5. Find the quotient and the divisor.$
Word Problems and Applications

March 2020

5 q

Q1(A)(ii) $From the following equations, which one is the quadratic equation?$
Tap an option to check your answer.
Roots of a Quadratic Equation
Q1(B)(iii) $a$
Roots of a Quadratic Equation
Q2(B)(ii) $x^{2} - 15x + 54 = 0$
Solving by Factorisation
Q4(iii) $The sum of the areas of two squares is 400 sq.m. If the difference between their perimeters is 16 m, find the sides of the two squares.$
Word Problems and Applications
Q5(ii) $\text{Rs.}\,24$
Word Problems and Applications

March 2019

4 q

Q2(A)(ii) $x^{2} + 10x - 7 = 0$
Tap an option to check your answer.
Standard Form of a Quadratic Equation
Q2(B)(iii) $x^{2} + 8x + 15 = 0$
Solving by Factorisation
Q3(B)(ii) $-3$
Relation between Roots and Coefficients
Q5(ii) $3\frac{1}{13}$
Word Problems and Applications

March 2018

5 q

Q1(ii) $\dfrac{5}{4}m^2 - 7 = 0$
Roots of a Quadratic Equation
Q2(ii) $x^2 - 10x + k = 0$
Roots of a Quadratic Equation
Q2(v) $-6$
Relation between Roots and Coefficients
Q3(ii) $3x^2 + 2x = 1$
Solving by Formula and Completing the Square
Q4(i) $\alpha + \beta = 5$
Relation between Roots and Coefficients

March 2017

5 q

Q1(ii) $3 - 2\sqrt{5}$
Roots of a Quadratic Equation
Q1(vi) $a, b, c$
Standard Form of a Quadratic Equation
Q2(ii) $(\Delta)$
Nature of Roots (Discriminant)
Q3(ii) $3x^2 - 22x + 40 = 0$
Solving by Factorisation
Q5(i) $If the cost of bananas is increased by Rs 10 per dozen, one can get 3 dozen less for Rs 600. Find the original cost of one dozen of bananas.$
Word Problems and Applications

March 2016

5 q

Q1(ii) $a$
Roots of a Quadratic Equation
Q1(iii) $-2$
Relation between Roots and Coefficients
Q2(ii) $x^2 + 7x + 10 = 0$
Solving by Factorisation
Q3(i) $5m^2 + 5m - 1 = 0$
Solving by Formula and Completing the Square
Q5(i) $6123$
Word Problems and Applications

The 10 board questions to practise first

The questions the board asked again come first, most asked first. Each one says how often and when.

Question 1
Asked 4 times: Mar 2020*, Mar 2022, Jul 2024, Mar 2025 (* = numbers or wording changed that year)
Q1(A)(ii) $खालीलपैकी कोणते समीकरण वर्गसमीकरण आहे ? From the following equations which one is the quadratic equation?$
Tap an option to check your answer.
Question 2
Asked 3 times: Mar 2022, Mar 2024, Mar 2026
Q2(B)(iii) $x^2 + x - 20 = 0$
Question 3
Asked 3 times: Mar 2023, Jul 2025, Mar 2026
Q1(B)(iv) $ax^2 + bx + c = 0$
Question 4
Asked 2 times: Mar 2023, Mar 2026
Q1(A)(ii) $खालीलपैकी कोणते समीकरण वर्गसमीकरण नाही ? Out of the following equations which one is not a quadratic equation?$
Tap an option to check your answer.
Question 5
Asked 2 times: Mar 2018*, Mar 2026 (* = numbers or wording changed that year)
Q4(i) $एका वर्गसमीकरणाच्या दोन मुळांची बेरीज 7 आणि त्यांच्या घनांची बेरीज 91 आहे तर ते वर्गसमीकरण कोणते ? The sum of two roots of a quadratic equation is 7 and sum of their cubes is 91, find the equation.$
Question 6
Asked 2 times: Mar 2020, Jul 2025
Q2(B)(ii) $x^2 - 15x + 54 = 0$
Question 7
Asked 2 times: Mar 2022, Jul 2024
Q2(B)(ii) $x = 3$
Question 8
Asked 2 times: Mar 2019*, Mar 2024 (* = numbers or wording changed that year)
Q4(i) $एक टाकी दोन नळाच्या साहाय्याने 6 तासात पूर्ण भरते. ती टाकी भरण्यास लहान नळाला मोठ्या नळापेक्षा 5 तास जास्त लागतात तर प्रत्येक नळाने ती टाकी भरण्यास किती वेळ लागेल ? A tank can be filled up by two taps in 6 hours. The smaller tap alone takes 5 hours more than the bigger tap alone. Find the time required by each tap to fill the tank separately.$
Question 9
Asked 2 times: Mar 2022, Mar 2023
Q3(B)(ii) $x^2 + 10x + 2 = 0$
Question 10
This type asked 7 times: Mar 2016, Mar 2018, Mar 2022, Mar 2024, Jul 2024, Mar 2025, Jun 2026. This one: Jun 2026
Q3(B)(ii) $x^2 - 3x - 2 = 0$

Standard form of quadratic equation

Solved Examples

Roots of a quadratic equation

Solved Example

Practice Set 2.1

Solutions of a quadratic equation by factorisation

Solved Examples

Practice Set 2.2

Solution of a quadratic equation by completing the square

Solved Examples

Practice Set 2.3

Formula for solving a quadratic equation

Solved Examples

Practice Set 2.4

Nature of roots of a quadratic equation

Solved examples

The relation between roots of the quadratic equation and coefficients

Solved examples

To obtain a quadratic equation having given roots

Solved examples

Practice Set 2.5

Application of quadratic equation

Solved examples

Practice Set 2.6

Problem Set 2

What the board has asked from this chapter

June 2026

March 2026

July 2025

March 2025

July 2024

March 2024

March 2023

March 2022

March 2020

March 2019

March 2018

March 2017

March 2016

The 10 board questions to practise first

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10