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 VII Mathematics

Class VII Mathematics

Chapter 12: Algebraic Expressions

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 VII Mathematics: Algebraic Expressions. 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

Algebra BasicsSimple Equations

Detailed Subtopics Study Guide

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

1Terms, factors, and coefficients

Concept Explanation

Terms are parts of an expression separated by + or - signs. Factors are variables or numbers multiplied to form terms. The numerical factor is the coefficient.

Mathematical Representation

\text{In } 3x^2 - 5x: \text{ Terms: } 3x^2, -5x; \, \text{ Coefficient of } x = -5

Study Guideline: Keep the negative sign with the term and its coefficient (e.g., the coefficient of x in 5 - x is -1).

2Monomials, binomials, trinomials, and polynomials

Concept Explanation

Monomial has 1 term. Binomial has 2 terms. Trinomial has 3 terms. Polynomial has one or more terms with non-negative integer exponents.

Mathematical Representation

\text{Mono: } ax^n; \, \text{ Bi: } ax^n + bx^m; \, \text{ Tri: } ax^n + bx^m + c

Study Guideline: Terms must be unlike to classify expressions (e.g., 2x + 3x is a monomial because it simplifies to 5x).

3Addition and subtraction of algebraic expressions

Concept Explanation

Add or subtract algebraic expressions by grouping like terms and calculating their coefficients.

Mathematical Representation

(3x+5y) + (2x-3y) = (3+2)x + (5-3)y = 5x + 2y

Study Guideline: When subtracting, change the sign of every term in the expression being subtracted.

4Evaluating expressions values

Concept Explanation

Finding the numerical value of an algebraic expression by substituting given values for variables.

Mathematical Representation

f(x) = ax^2 + bx + c \implies \text{Substitute } x = k

Study Guideline: Use parentheses when substituting negative numbers (e.g. x = -2 in x² becomes (-2)² = 4).