Unit 2 Class 10 Math New Book Solutions

Unit 2 Class 10 Math New Book Solutions are available here in easy PDF format. This unit is titled Quadratic Equations and Inequalities and includes Exercise 2.1 to Exercise 2.7 and Review Exercise 2. These step-by-step solved notes help students understand quadratic equations, graphical solutions, roots and coefficients, discriminant, quadratic inequalities, formulas, and real-life applications. Students can use these Unit 2 solved PDFs for homework, school tests, monthly tests, final exams, and board exam revision.

PDF Solutions of Unit 2 Class 10 Math New Book

These Unit 2 Class 10 Math New Book Solutions are arranged exercise-wise so that students can open the exact PDF they need.

Table Of Contents

Quick Overview of Unit 2 Exercises

What is Unit 2 Class 10 Math New Book About?

Unit 2 of the Class 10 Math New Book is about quadratic equations and related algebraic ideas. In this unit, students learn how to write quadratic equations in standard form, solve them by different methods, understand roots, use the discriminant, solve quadratic inequalities, rearrange formulas, and apply quadratic equations in real-life situations.

A quadratic equation is an equation in which the highest power of the variable is 2.

The standard form is:

ax² + bx + c = 0

Here, a, b, and c are real numbers and a ≠ 0.

For example:

x² + 5x + 6 = 0

This is a quadratic equation because the highest power of x is 2.

Unit 2 is important because many exam questions can be taken from this unit. It includes short questions, MCQs, long questions, graphical questions, formula-based questions, inequalities, and word problems.

Solutions of Exercise 2.1 Class 10 Math New Book

Solutions of Exercise 2.2 Class 10 Math New Book

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Solutions of Exercise 2.3 Class 10 Math New Book

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Solutions of Exercise 2.4 Class 10 Math New Book

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Solutions of Exercise 2.5 Class 10 Math New Book

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Solutions of Exercise 2.6 Class 10 Math New Book

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Solutions of Exercise 2.7 Class 10 Math New Book

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Solutions of Review Exercise 2 Class 10 Math New Book

Important Definitions of Unit 2

Quadratic Equation

An equation in which the highest power of the variable is 2 is called a quadratic equation. For a detailed explanation of this topic, read our complete guide on Quadratic Equations.

For example:

x² + 5x + 6 = 0

Standard Form of Quadratic Equation

The standard form of a quadratic equation is:

ax² + bx + c = 0

where a, b, and c are real numbers and a ≠ 0.

Roots of a Quadratic Equation

The values of x that satisfy a quadratic equation are called its roots. For a complete explanation, read our guide on Roots of a Quadratic Equation.

For example, if:

(x − 2)(x − 3) = 0

then the roots are:

x = 2 and x = 3

Discriminant

The discriminant of a quadratic equation is:

D = b² − 4ac

It tells us about the nature of roots.

Quadratic Inequality

A quadratic inequality is an inequality that contains a quadratic expression.

For example:

x² + 3x − 4 > 0

Critical Points

Critical points are the values obtained by putting each factor equal to zero while solving an inequality.

For example:

(x + 4)(x − 1) > 0

Critical points are:

x = −4 and x = 1

Subject of a Formula

The variable which is written alone on one side of a formula is called the subject of the formula.

For example, in:

v = u + at

v is the subject of the formula.

Important Formulas of Unit 2

Students should revise these formulas again and again.

Standard Form

ax² + bx + c = 0

where a ≠ 0

Quadratic Formula

x = (-b ± √(b² − 4ac)) / 2a

Example of Quadratic Formula

Solve:

2x² − 5x + 3 = 0

Here:

a = 2, b = −5, c = 3

Using the quadratic formula:

x = (-b ± √(b² − 4ac)) / 2a

x = (-(-5) ± √((-5)² − 4(2)(3))) / 2(2)

x = (5 ± √(25 − 24)) / 4

x = (5 ± 1) / 4

So:

x = 3/2 or x = 1

Therefore:

Solution set = {1, 3/2}

Discriminant

D = b² − 4ac

Nature of Roots

D > 0 means roots are real and unequal.

D = 0 means roots are real and equal.

D < 0 means roots are imaginary.

D > 0 and perfect square means roots are rational and unequal.

D > 0 and not a perfect square means roots are irrational and unequal.

Sum and Product of Roots

For ax² + bx + c = 0:

Sum of roots = −b/a

Product of roots = c/a

Example of Sum and Product of Roots

For the equation:

3x² + 5x − 12 = 0

Here:

a = 3, b = 5, c = −12

Sum of roots = −b/a

Sum of roots = −5/3

Product of roots = c/a

Product of roots = −12/3

Product of roots = −4

So, the sum of roots is −5/3 and the product of roots is −4.

Equation from Roots

If α and β are roots, then:

x² − (α + β)x + αβ = 0

Maximum or Minimum Value

For:

f(x) = ax² + bx + c

the maximum or minimum occurs at:

x = −b/2a

If a < 0, maximum value occurs.

If a > 0, minimum value occurs.

Short Revision Table of Unit 2

Concept	Key Rule	Example
Quadratic equation	Highest power is 2	x² + 5x + 6 = 0
Standard form	ax² + bx + c = 0	2x² − 3x + 1 = 0
Factorization	Split the middle term	x² − 5x + 6 = 0
Quadratic formula	Use a, b, c in formula	x = (-b ± √(b² − 4ac)) / 2a
Discriminant	D = b² − 4ac	Used to check nature of roots
Equal roots	D = 0	Roots are same
Real unequal roots	D > 0	Roots are different
Imaginary roots	D < 0	No real roots
Equation from roots	x² − (sum)x + product = 0	roots 2, 3 give x² − 5x + 6 = 0
Quadratic inequality	Use critical points	(x − 1)(x − 3) > 0
Subject of formula	Keep required variable alone	y = mx + c gives x = (y − c)/m
Maximum value	x = −b/2a when a < 0	Profit or height questions

Common Mistakes Students Make in Unit 2

Not Writing the Equation in Standard Form

Many students start solving without arranging the equation in standard form.

Always write the equation as:

ax² + bx + c = 0

before applying factorization, quadratic formula, or discriminant.

Wrong Signs in Factorization

Students often make mistakes while splitting the middle term.

For example:

x² − x − 6 = 0

The correct split is:

x² − 3x + 2x − 6 = 0

because −3 + 2 = −1 and (−3)(2) = −6.

Forgetting ± in Square Root

When taking square root, students should remember both positive and negative values.

For example:

x² = 9

x = ±3

Do not write only x = 3.

Using Wrong Values of a, b, and c

In the quadratic formula and discriminant, students must identify a, b, and c correctly.

For example, in:

2x² − 5x + 3 = 0

a = 2, b = −5, c = 3

The negative sign with b is important.

Confusing Sum and Product of Roots

For ax² + bx + c = 0:

Sum of roots = −b/a

Product of roots = c/a

Students often forget the negative sign in the sum of roots.

Choosing Wrong Intervals in Inequalities

In quadratic inequalities, finding the critical points is not enough. Students must also check the sign of each interval.

For example, if:

(x + 4)(x − 1) > 0

then the answer is outside the roots:

(−∞, −4) ∪ (1, ∞)

not between the roots.

Forgetting to Change the Inequality Sign

When multiplying or dividing an inequality by a negative number, the inequality sign changes.

For example:

−2x > 6

x < −3

Drawing Graphs Without Scale

In graphical questions, students should choose a proper scale. If the scale is not clear, the graph may give a wrong answer.

Always label the x-axis, y-axis, points, line, and curve clearly.

Making Formula Rearrangement Too Quickly

In Exercise 2.6, students often try to move terms without showing proper steps.

It is better to use the same operation on both sides and write each step clearly.

How to Use These Notes

These notes are not only for copying answers. They are prepared to help students understand the method.

First, read the basic explanation of the exercise.

Then try to solve the question yourself.

After that, open the PDF solution and compare your work.

If your answer is wrong, check the exact step where the mistake happened.

Then solve the same question again without looking at the solution.

For best results, students should first revise the formulas, then solve the exercise, then check the PDF solution. This method will help in tests and exams.

Exam Importance of Unit 2

Unit 2 is important for exams because it includes many types of questions. Students can get MCQs, short questions, and long questions from this unit.

Exercise 2.1 is important because it includes solving quadratic equations by different methods. Students should practise factorization, completing the square method, and quadratic formula.

Exercise 2.2 is important for graphical questions. Students should know how to make a table of values, plot points, draw graphs, and find the point of intersection.

Exercise 2.3 is important because questions about roots and coefficients are common. Students should remember the sum and product of roots formulas.

Exercise 2.4 is important for MCQs and short questions. The discriminant helps students find whether roots are real, equal, unequal, rational, irrational, or imaginary.

Exercise 2.5 is important because quadratic inequalities need careful steps. Students should know how to find critical points and choose the correct interval.

Exercise 2.6 is useful for short questions because it is based on making a variable the subject of a formula.

Exercise 2.7 is important for word problems and real-life applications. Students should practise maximum and minimum value questions carefully.

Review Exercise 2 is best for final revision because it includes MCQs and written questions from the whole unit.

Exam Preparation Tips for Unit 2

Unit 2 becomes easy when students practise the basic rules again and again.

For MCQs, revise standard form, discriminant, nature of roots, sum of roots, product of roots, and subject of formula.

For short questions, learn definitions and formulas clearly.

For long questions, practise solving quadratic equations by factorization, completing square method, and quadratic formula.

For graphical questions, practise making tables of values and drawing graphs neatly.

For inequalities, always find critical points and check intervals.

For real-life questions, read the statement carefully and identify what is given and what is required.

Before exams, solve Review Exercise 2 as a complete revision test. It includes many important concepts of the unit.

Related Class 10 Math Resources

Quadratic equations are one of the most important topics in Class 10 Mathematics. To practise this unit more, students can also use our Quadratic Equation Solver. It helps students check roots, discriminant, and solution steps.

Students who want to revise algebra basics can also use our Simultaneous Equations Solver. It is useful for graphical method and equation-based practice.

If students want to revise the previous unit, they can also study Unit 1 Complex Numbers Class 10 Math New Book Solutions.

FAQs About Unit 2 Class 10 Math New Book Solutions

What is Unit 2 of Class 10 Math New Book about?

Unit 2 is about quadratic equations and related topics. It includes standard form, algebraic solution methods, graphical method, roots and coefficients, discriminant, quadratic inequalities, subject of formula, and real-life applications.

Are these solutions according to the new Class 10 Math book?

Yes, these solutions are prepared according to the new Class 10 Mathematics book for the 2026–27 session.

How many exercises are included in Unit 2?

Unit 2 includes Exercise 2.1, Exercise 2.2, Exercise 2.3, Exercise 2.4, Exercise 2.5, Exercise 2.6, Exercise 2.7, and Review Exercise 2.

Can I download the PDF solutions?

Yes, students can view the PDF solutions online and download them for offline study.

What is the standard form of a quadratic equation?

The standard form of a quadratic equation is:

ax² + bx + c = 0

where a ≠ 0.

What is the quadratic formula?

The quadratic formula is:

x = (-b ± √(b² − 4ac)) / 2a

It is used to solve quadratic equations.

What is the completing the square method?

Completing the square is a method used to solve quadratic equations. In this method, we change the quadratic expression into a perfect square form.

For example:

x² + 6x + 5 = 0

First move the constant term:

x² + 6x = −5

Half of 6 is 3, and 3² = 9.

Add 9 on both sides:

x² + 6x + 9 = −5 + 9

(x + 3)² = 4

Now take square root:

x + 3 = ±2

So:

x = −3 ± 2

Therefore:

x = −1 or x = −5

What is the discriminant?

The discriminant is:

D = b² − 4ac

It tells us about the nature of roots of a quadratic equation.

What is the difference between real and imaginary roots?

Real roots are values of x that belong to the real number system. Imaginary roots are not real number values.

The discriminant helps us identify the type of roots.

For a quadratic equation:

ax² + bx + c = 0

D = b² − 4ac

If D > 0, the roots are real and unequal.

If D = 0, the roots are real and equal.

If D < 0, the roots are imaginary.

For example, if D = −24, then the roots are imaginary because the discriminant is less than zero.

Which exercise is about quadratic inequalities?

Exercise 2.5 is about solving quadratic inequalities using critical points and sign intervals.

Which exercise is about real-life applications?

Exercise 2.7 is about real-life applications of quadratic equations, maximum values, and quadratic inequalities.

Which exercise is most important for exams?

All exercises are important. Exercise 2.1, Exercise 2.3, Exercise 2.4, Exercise 2.5, Exercise 2.7, and Review Exercise 2 are especially important because they include solution methods, roots, discriminant, inequalities, applications, and mixed revision.

How should I prepare Unit 2 for exams?

First revise all formulas. Then solve Exercise 2.1 to Exercise 2.7. After that, solve Review Exercise 2 without looking at the solution. Also revise common mistakes so that you do not repeat them in exams.

Disclaimer

These solved notes are prepared by notesofmath.com for educational help only. We are not affiliated with any textbook board or official publisher. Every effort has been made to keep the solutions correct and easy to understand. Students should also consult their official textbook, classroom teacher, and school instructions for final exam preparation.

Final Words

Unit 2 is an important unit of the Class 10 Math New Book. It may look lengthy at first because it includes quadratic equations, graphs, roots, discriminant, inequalities, formulas, and applications. But when students practise one exercise at a time, the whole unit becomes easy.

Use the PDF solutions for step-by-step practice. Revise the formulas daily. Try to solve every question yourself before checking the answer. If you make a mistake, do not worry. Find the wrong step, correct it, and practise again.

With regular practice, students can prepare Unit 2 completely and confidently.