4 Common Mistakes in ICSE Class 10 Chapter Quadratic Equations

In this blog, we explore the world of quadratic equations, highlighting the stumbling blocks that often shut students down. It aims to demystify the subject by identifying and solving the most common mistakes students make.

By Topperlearning Expert 22nd Feb, 2024 | 11:08 am

Quadratic equations are the cornerstone of algebra, because they form the basis of mathematical formulas. Regardless of the specialized role, students often encounter multiple difficulties while solving quadratic equations.

So let’ us break down the intricacies of quadratic equations, identify common mistakes, and come up with some valuable insights that will help us to solve the challenges. Understanding this trick will better prepare you to do it to not only avoid the pitfalls but to master the art of solving quadratic equations with confidence.

Overview of Quadratic Equations:

1. Introduction

2.

Roots of Quadratic Equations	Nature of Roots
A number α ∈ R is said to be a solution/root of the quadratic equation if aα² + bα + c = 0.	The nature of the roots depends on D = b² – 4ac If D > 0, roots are real & unequal If D < 0, roots are real & imaginary. If D = 0, roots are real & equal.

3. Solution of Quadratic Equation
Solution of a quadratic equation can be obtained using the following methods:

Factorisation Method
By factorising the quadratic polynomial.
Quadratic Formula Method
Using the formula i.e. $begin mathsize 11px style x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction end style$

For more details, click Revision notes on Quadratic Equations.

Let’s now start discussing the mistakes made by the students.

Mistake 1: Fail to apply the condition that the root of an equation satisfies it

Root of an equation satisfies the equation. So, root of a quadratic equation satisfies the quadratic equation.
Most of the students fail to apply this knowledge and so don’t get the required answer.This is shown below with an example.
Example: Find the value of ‘p’ if ‘3’ is a root of the equation “x² – px + 3 = 0”.

Mistake 2: Applying Quadratic Formula incorrectly

Many a times, students write an incorrect quadratic formula or put incorrect values in the correct quadratic formula which results into incorrect answer.
This is shown with an example below:

Mistake 3: Taking incomplete value of the square root in decimal form

When we take the incomplete value of the square root, we get an incorrect answer in both the cases that is either if we round of or not.

This is shown below with an example:

Example: Solve the quadratic equation x² + 4x – 8 = 0 and give your answer correct to one decimal place.

Mistake 4: Incorrectly rounding off the final value of the variable

When the root of the quadratic equation is a decimal, students many a time round off incorrectly.
This is shown with the same example as above:

Conclusion:

We can conclude that when dealing with quadratic equations can be challenging, a clear understanding of the common errors and the knowledge gained in this blog will drive you to tackle the complexities. You have to stay focused and not miss any information when attempting questions. May your mathematical journey be filled with curiosity, resilience and ultimately triumph, over the intricacies of equations. Avoid making such mistakes by practising questions available.
Understand the concepts through Revision Notes and Videos. Practice a variety of questions like Multiple Choice Questions, Subjective Questions and Assertion & Reasoning Questions. You can also use Sample Papers to get an idea of the actual paper. All of these resources are available for Maharashtra, CBSE and ICSE Boards students at TopperLearning.