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 IX Mathematics

Class IX Mathematics

Chapter 4: Linear Equations in Two Variables

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

Linear Equation Solver (2 Variables)

Solve systems of two linear equations with two variables: a1x + b1y = c1 and a2x + b2y = c2.

Live Solver

Adjust Inputs

a1 (Eq 1 x Coeff)2

b1 (Eq 1 y Coeff)1

c1 (Eq 1 Constant)8

a2 (Eq 2 x Coeff)1

b2 (Eq 2 y Coeff)-1

c2 (Eq 2 Constant)1

Calculated Results

Solved Variable (x)

Solved Variable (y)

Student Solver & Visualizer Guide

Real-time calculations

Step-by-step solving

1. Collect input parameters:

- a1 = 2

- b1 = 1

- c1 = 8

- a2 = 1

- b2 = -1

- c2 = 1

2. Feed parameters through standard algorithmic calculation methods.

3. Compile calculated results:

- solveX = 3

- solveY = 2

Student-friendly explanations

"This math utility processes input parameters using standard algebraic algorithms. By substituting variables into target formulas, the engine solves equations and computes results instantly with high arithmetic precision!"

Visual explanations

MATH SOLVER RUNNING:
 [Inputs] ──► [Mathematical Formula] ──► [Outputs]
  Processed elements successfully.