Can a quadratic equation have three roots?

No. According to the Fundamental Theorem of Algebra, a polynomial equation of degree n has exactly n complex roots. A quadratic equation is a second-degree polynomial (n = 2) and thus can have at most two roots.

What are imaginary roots?

When the discriminant D = b² - 4ac is negative, the square root term contains a negative value, yielding roots with the imaginary unit i (where i = √-1). These are complex numbers representing points where the parabola does not cross the x-axis.

Back to Class VI Mathematics

Class VI Mathematics

Chapter 10: Algebra Basics

Standard NCERT & CBSE aligned study curriculum. Master concepts, track accuracy, revise weak areas, and challenge yourself with 9 customized practice modes.

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Syllabus Sections

Chapter Overview

Welcome to Class VI Mathematics: Algebra Basics. This chapter forms a core structural component of the math syllabus, designed to build analytical rigor and key formula models.

Use the detailed subtopic guide below to review standard definitions, key mathematical rules, and study guidelines.

Prerequisite Concepts

Whole NumbersPlay with Patterns

Detailed Subtopics Study Guide

Review detailed conceptual explanations, mathematical equations, and guidelines for each subtopic in this chapter:

1Introduction to variables

Concept Explanation

Variables are letters (like x, y, n) used to represent unknown values or quantities that can change.

Mathematical Representation

x \in S

Study Guideline: A variable has no fixed numerical value, unlike a constant.

2Matchstick patterns

Concept Explanation

Using matchsticks to construct repeating shapes, modeling the relationship between the shape count and matchsticks needed using algebraic rules.

Mathematical Representation

M = an + b \quad (\text{e.g. } M = 3n + 1 \text{ for triangles sequence})

Study Guideline: Identify the number of matchsticks added for each new shape to find the coefficient of n.

3Algebraic expressions variables

Concept Explanation

Forming expressions combining constants, variables, and operations.

Mathematical Representation

ax + b \quad (\text{where } a, b \text{ are constants, } x \text{ is variable})

Study Guideline: Expressions do not contain an equals sign.

4Writing equations

Concept Explanation

Translating mathematical statements of equality into equations containing variables and an equals sign (=).

Mathematical Representation

f(x) = C

Study Guideline: An equation must have an equals sign (=) separating Left Hand Side (LHS) and Right Hand Side (RHS).