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 3: Pair of Linear Equations in Two Variables

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• Title: Class X Math: Pair of Linear Equations in Two Variables Printable Sheet
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• Sections: Formulas checklist, 5 assessment questions, worked keys

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Class X Mathematics: Pair of Linear Equations in Two Variables

Name: ______________________Date: __________________Score: ______ / 5

Section I: Key Formulas

System Consistency condition

\frac{a_1}{a_2} \neq \frac{b_1}{b_2}

Infinite Solutions condition

\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}