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.

Select Syllabus Tab:

Syllabus Sections

Key Formulas & Equations

Click Copy to duplicate

Standard Linear solution

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

Formula to solve basic linear equations.

Related Formulas from Adjacent Chapters

Additive Inverse

\frac{a}{b} + \left(-\frac{a}{b}\right) = 0

[From Rational Numbers] Sum of a rational number and its additive inverse is zero.

Multiplicative Reciprocal

\frac{a}{b} \times \frac{b}{a} = 1

[From Rational Numbers] Product of a rational number and its reciprocal is one.

Interior Angle Sum

S = (n - 2) \times 180^\circ

[From Understanding Quadrilaterals] Interior angle sum of an n-sided polygon.

Exterior Angle Sum

S_{ext} = 360^\circ

[From Understanding Quadrilaterals] Exterior angles of any convex polygon always sum to 360 degrees.