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 2: Linear Equations in One Variable

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: Linear Equations in One Variable. 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

Simple Equations

Detailed Subtopics Study Guide

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

1Linear algebraic equations

Concept Explanation

A linear equation in one variable has a single variable with a maximum exponent of 1. Solving it finds the root.

Mathematical Representation

ax + b = 0 \implies x = -\frac{b}{a}

Study Guideline: Gather variable terms on one side and constant terms on the other to solve.

2Solving equations with variable on both sides

Concept Explanation

Solving linear equations where the variable appears on both left and right-hand sides, requiring grouping variable terms together.

Mathematical Representation

ax + b = cx + d \implies (a-c)x = d - b \implies x = \frac{d-b}{a-c}

Study Guideline: Transpose all variable terms to LHS and all constants to RHS, then solve.

3Reducing equations to simpler form

Concept Explanation

Simplifying complex equations (often containing fractions or brackets) by finding common denominators and expanding parentheses.

Mathematical Representation

a(x-b) = c(x-d) \implies ax - ab = cx - cd

Study Guideline: Multiply by the LCM of all denominators to eliminate fractional terms in one step.

4Real-world linear applications

Concept Explanation

Using linear equations to solve real-world problems about ages, digit places, money, mixtures, and speed.

Mathematical Representation

\text{Model: } f(x) = C \implies \text{Solve for } x

Study Guideline: Translate English phrases carefully: 'twice a number' is 2x; 'two consecutive numbers' are x and x+1.