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 4: Simple Equations

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: Simple Equations. 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 Basics

Detailed Subtopics Study Guide

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

1Setting up equations

Concept Explanation

Translating word problems into mathematical equations with variables and constants.

Mathematical Representation

ax + b = c

Study Guideline: Identify what is unknown, assign it a variable (like x), and match statements with algebraic operations.

2Solving equations by variable separation

Concept Explanation

Solving simple equations by performing inverse operations on both sides to isolate the variable.

Mathematical Representation

x + a = b \implies (x + a) - a = b - a \implies x = b - a

Study Guideline: Perform the exact same operation on both sides of the equals sign to keep the balance.

3Transposing variables

Concept Explanation

Transposition is moving terms from one side of an equation to another, changing their operation to its inverse.

Mathematical Representation

x - a = b \implies x = b + a; \quad \frac{x}{a} = b \implies x = ab

Study Guideline: Transposed terms change operations: + to -, - to +, × to ÷, and ÷ to ×.

4Applications to word problems

Concept Explanation

Using linear equations to solve real-world problems involving ages, numbers, geometry, and finance.

Mathematical Representation

\text{Solve: } f(x) = C \implies \text{Substitute to check}

Study Guideline: Always read the final question to make sure you state what the variable solution represents in context.