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3.Quadratic Equations & Roots
Class 11 • Mathematics • NCERT
Quadratic Equations & Roots
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This lesson explains quadratic equations and their roots as per NCERT Class 11. Students learn the standard form, methods to find roots, and the nature of roots using the discriminant.
Lesson Objectives
- Understand the standard form of a quadratic equation.
- Define roots of a quadratic equation.
- Use the quadratic formula.
- Determine the nature of roots.
1. Quadratic Equation
A quadratic equation in one variable x is an equation of the form:
ax² + bx + c = 0, where a ≠ 0
2. Roots of a Quadratic Equation
The values of x that satisfy the quadratic equation are called its roots.
A quadratic equation has two roots (real or complex).
3. Quadratic Formula
The roots of the quadratic equation ax² + bx + c = 0 are given by:
x = [−b ± √(b² − 4ac)] / 2a
4. Discriminant & Nature of Roots
The expression b² − 4ac is called the discriminant (D).
If D > 0 → Two distinct real roots
If D = 0 → Two equal real roots
If D < 0 → Two complex roots
If D = 0 → Two equal real roots
If D < 0 → Two complex roots
5. Simple NCERT Example
Solve: x² − 5x + 6 = 0
Roots are x = 2 and x = 3
Roots are x = 2 and x = 3
Practice Questions (NCERT)
- Write the standard form of a quadratic equation.
- What condition must a satisfy?
- Define roots of a quadratic equation.
- Write the quadratic formula.
- What is the discriminant?
- Find D for x² − 4x + 4 = 0.
- How many roots does a quadratic equation have?
- What happens if D = 0?
- Are complex roots possible?
- Is this topic part of NCERT Class 11?
✅ Show Answer Key
- ax² + bx + c = 0
- a ≠ 0
- Values of x that satisfy the equation.
- x = [−b ± √(b² − 4ac)] / 2a
- b² − 4ac
- 0
- Two
- Two equal real roots
- Yes
- Yes
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