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 VIII Mathematics

Class VIII Mathematics

Chapter 8: Algebraic Expressions and Identities

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 VIII Mathematics: Algebraic Expressions and Identities. 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

Algebraic ExpressionsAlgebra Basics

Detailed Subtopics Study Guide

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

1Terms and factors variables

Concept Explanation

Terms are components added to build expressions. Factors are numbers/variables multiplied together to build terms.

Mathematical Representation

\text{Expression } = \sum T_i \quad (T_i = \prod f_{i,j})

Study Guideline: Like terms share the exact same variable factors and powers.

2Multiplication of expressions: binomial by binomial

Concept Explanation

Multiplying two binomials is done by distributing each term of the first binomial over the second (FOIL method).

Mathematical Representation

(a+b)(c+d) = ac + ad + bc + bd

Study Guideline: Multiply First, Outer, Inner, and Last terms, and then simplify like terms.

3Standard Identities: (a+b)², (a-b)², a²-b²

Concept Explanation

Standard algebraic identities are equality relations true for all values of variables, used for expansions and factorization.

Mathematical Representation

(a+b)^2 = a^2 + 2ab + b^2, \quad (a-b)^2 = a^2 - 2ab + b^2, \quad a^2 - b^2 = (a-b)(a+b)

Study Guideline: Write as (a+b)² = a² + 2ab + b² and (a-b)² = a² - 2ab + b².

4Applying identities for numerical calculation

Concept Explanation

Using standard identities to simplify arithmetic products (e.g. 99² = (100 - 1)²).

Mathematical Representation

99^2 = (100-1)^2 = 10000 - 200 + 1 = 9801

Study Guideline: Break the number into a sum or difference of a multiple of 10 before applying the identity.