📘 Chapter 4: Quadratic Equations – Class 10 Maths Notes

 Introduction:

Welcome to our Class 10 Maths Notes! In this post, we cover Chapter 4: Quadratic Equations in detail. Whether you're preparing for your board exams or just revising key concepts, this guide has everything you need – definitions, formulas, methods to solve, and example questions. Let’s dive in!

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📘 What is a Quadratic Equation?

A quadratic equation is a polynomial equation of degree 2. The standard form is:

$$ax^2 + bx + c = 0 \quad (a ≠ 0)$$

Here,

• $a, b, c$ are real numbers

• $x$ is the variable

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🔢 Methods to Solve Quadratic Equations:

There are three main methods to solve quadratic equations:

1. Factorization Method

• Express the equation as a product of two binomials.

• Set each factor to zero and solve for $x$.

2. Completing the Square

• Rearrange the equation in the form $(x + p)^2 = q$.

• Then solve using square roots.

3. Quadratic Formula

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

This method is useful when factorization is not possible.

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📌 Important Formulas:

• Discriminant (D):

  $$D = b^2 - 4ac$$

  • If D > 0: Two real and distinct roots

  • If D = 0: Two real and equal roots

  • If D < 0: No real roots (complex roots)

• Roots using Quadratic Formula:

  $$x = \frac{-b \pm \sqrt{D}}{2a}$$

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✍️ Example Problems:

Example 1:
Solve: $x^2 - 5x + 6 = 0$
Solution:
Factorizing: $(x - 2)(x - 3) = 0$
So, $x = 2$ or $x = 3$

Example 2:
Solve using quadratic formula: $2x^2 - 4x - 6 = 0$
Here, $a = 2$, $b = -4$, $c = -6$

$$D = (-4)^2 - 4(2)(-6) = 16 + 48 = 64$$ $$x = \frac{-(-4) \pm \sqrt{64}}{2(2)} = \frac{4 \pm 8}{4}$$ $$x = 3 \quad \text{or} \quad x = -1$$

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📝 Tips to Remember:

• Always simplify the equation to standard form before solving.

• Check the discriminant to know the nature of roots.

• Practice solving using all three methods to gain confidence.

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Conclusion:

Quadratic Equations are an important part of Class 10 Maths. With the right understanding and enough practice, you can easily master this chapter. Keep revising key formulas and solving different types of questions to boost your preparation!

👉 Don't forget to bookmark this page for quick revision before your exams!