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.

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Class X Mathematics

Chapter 4: Quadratic 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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Worksheet Details:

• Title: Class X Math: Quadratic Equations Printable Sheet
• Format: Print Optimized CSS stylesheet
• Sections: Formulas checklist, 5 assessment questions, worked keys

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Class X Mathematics: Quadratic Equations

Name: ______________________Date: __________________Score: ______ / 5

Section I: Key Formulas

The Quadratic Formula

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Discriminant

D = b^2 - 4ac

Section II: Answer the Questions

1. Find the sum and product of the roots of the quadratic equation 2x² - 9x + 4 = 0. OR Find the discriminant of the quadratic equation 4x² - 5 = 0 and hence comment on the nature of roots of the equation.