Solutions of Unit 20 Class 10 Math Sindh Board
The Solutions of Unit 20 Class 10 Math Sindh Board are here — fully solved, exercise by exercise, and free to download. Unit 20 is called Theory of Quadratic Equations and it is one of the most important units in the Class 10 Mathematics book for Sindh Board students. Whether you are studying for your board exam or just want to understand the concepts, these notes will help you learn everything step by step.
Download Solutions — All Exercises
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What Is Unit 20 About?
Unit 20 of Class 10 Mathematics Sindh Board is all about going deeper into quadratic equations. Students do not just solve them here — they learn to understand the roots, predict their nature, find relationships between roots and coefficients, and even build new equations from scratch. This unit appears heavily in Sindh Board exams every year so it is very important to prepare it well.
The unit has seven exercises plus a review exercise. Each exercise focuses on a different concept and builds on the one before it
What Will You Learn in Unit 20?
Here is a quick overview of all the topics covered in this unit:
- How to find the discriminant and use it to decide the nature of roots
- All about cube roots of unity including ω and ω² and their properties
- The relationship between roots and coefficients of a quadratic equation
- How to evaluate symmetric functions of roots like α² + β² and α³ + β³
- How to form a new quadratic equation from given or transformed roots
- How to solve cubic and biquadratic equations when some roots are already known
- How to solve a system of two equations where one or both are quadratic
- How to apply quadratic equations to solve real life problems
How These Notes Help You
These Solutions of Unit 20 Class 10 Math Sindh Board have been prepared exercise by exercise covering every single question in Unit 20. Here is why they are useful:
- Every question is solved with complete step by step working — no steps are skipped
- The language is simple so even average students can follow along without any trouble
- Important formulas are clearly shown in each exercise so you do not have to search for them
- You can check your own work and find out exactly where you went wrong
- The notes follow the Sindh Board syllabus exactly so nothing is missing or extra
- Practicing from these notes builds confidence before the board exam
A Closer Look — What Each Exercise Covers
Exercise 20.1 — Nature of the Roots (Discriminant)
This exercise is the foundation of the whole unit. Here you will learn what the discriminant is and how the value of b² − 4ac tells you whether the roots of a quadratic equation are real, equal, or imaginary. You will also learn how to find unknown values in an equation when the nature of its roots is given. The solved notes show every step clearly so nothing feels confusing.
📥 Solutions of Exercise 20.1 — Click to View / Download
Exercise 20.2 — Cube Roots of Unity
In this exercise you will learn about the three cube roots of unity which are 1, ω, and ω². You will study their properties like 1 + ω + ω² = 0 and ω³ = 1 and use them to simplify expressions and solve problems. Many students find this topic tricky at first but the notes break everything down one property at a time so it becomes easy to understand and remember.
📥 Solutions of Exercise 20.2 — Click to View / Download
Exercise 20.3 — Roots and Coefficients
This is one of the most exam-important exercises in the whole unit. You will learn that for a quadratic equation ax² + bx + c = 0, the sum of roots equals −b/a and the product of roots equals c/a. Using this you can find the sum and product of roots without solving the equation. The notes also cover problems where special conditions are given on the roots such as when their sum equals a multiple of their product or when they differ by a given number.
📥 Solutions of Exercise 20.3 — Click to View / Download
Exercise 20.4 — Symmetric Functions of Roots
Here you will learn how to evaluate symmetric expressions involving the roots α and β such as α² + β², α³ + β³, and similar ones. Instead of finding the roots individually you use the sum and product of roots to calculate these expressions directly. The notes list every important identity and show a clear method so students do not lose marks on this topic in the exam.
📥 Solutions of Exercise 20.4 — Click to View / Download
Exercise 20.5 — Formation of Quadratic Equations
In this exercise you will learn how to build a quadratic equation when the roots are given. The formula used is x² − (sum of roots)x + (product of roots) = 0. The exercise also covers cases where the roots are transformed versions of the original roots such as 2α+1 and 2β+1, or α² and β², or 1/α and 1/β. The notes walk through every type one by one so students can handle any variation that appears in the exam.
📥 Solutions of Exercise 20.5 — Click to View / Download
Exercise 20.6 — Cubic and Biquadratic Equations
This exercise teaches you how to solve a cubic equation when one of its roots is already given and how to solve a biquadratic or quartic equation when two of its real roots are known. These question types look harder than they actually are. The notes show a clear and simple method for each type so students can solve them quickly and correctly.
📥 Solutions of Exercise 20.6 — Click to View / Download
Exercise 20.7 — Systems of Equations
In the final exercise you will learn how to solve a system of two equations in two variables. This includes cases where one equation is linear and the other is quadratic and also cases where both equations are quadratic. The exercise also includes real life word problems where you have to set up quadratic equations from a situation and then solve them. These types of problems often appear as the last question in Sindh Board exams.
📥 Solutions of Exercise 20.7 — Click to View / Download
Review Exercise — Unit 20
The review exercise brings together all the topics of Unit 20 in one place. It includes a mix of MCQs, short questions, and long questions. Solving this exercise after finishing all other exercises is the best way to prepare for the Sindh Board exam. The solved notes give you full working for every question so you can check your preparation and fix any weak areas before the exam.
📥 Solutions of Review Exercise — Click to View / Download
Quick Exam Tips for Unit 20
Before you sit the Sindh Board exam keep these tips in mind for Unit 20:
- Memorise the discriminant formula b² − 4ac and its three cases — this is guaranteed to come in the exam
- Learn the cube root of unity properties by heart especially 1 + ω + ω² = 0 and ω³ = 1
- Practice Vieta’s formulas sum = −b/a and product = c/a until they feel automatic
- For formation of equations always simplify the new sum and product before writing the final equation
- Show full working in your answer because Sindh Board gives marks for each step not just the final answer
- Do the Review Exercise last — it is the best practice test for this unit
Good luck with your exams. These Solutions of Unit 20 Class 10 Math Sindh Board are prepared specifically to help Sindh Board students understand every concept clearly and score well in their board exams. You should also visit our solutions of unit 19 of class 10 math Sindh Board. There is similar unit in the book of class 10 math Punjab Board named Unit 2: Theory of Quadratic Equations it covers these topics more in depth.